Hafdahl, Randall Sr. 1-31-2002 Lethal Injection Randall Huntsville, TX 826 Policeman  
 Haley, Thomas 7-10-1952 Electrocuted Tarrant Huntsville, TX 361 Rape  
 Hall, Wilburn 8-21-1957 Electrocuted Harris Huntsville, TX 401 Murder  
 Hamilton, Raymond 5-10-1935 Electrocuted Walker Huntsville, TX 147 Murder Elmwood Memorial Park
 Hammond, Karl 6-21-1995 Lethal Injection Bexar Huntsville, TX 865 Rape  
 Hampton, Bluitt 3-31-1940 Electrocuted Dallas Huntsville, TX 225 Murder  
 Handy, Placido 6-9-1940 Electrocuted Hidalgo Huntsville, TX 230 Murder  
 Hardin, Joe G. 5-31-1874 Lynched Comanche Comanche, TX n/a    
 Hardin, Tom 5-31-1874 Lynched Comanche Comanche, TX n/a    
 Harper, Benjamin 6-22-1917 Lynched Grimes Courtney, TX n/a  
 Harper, Julius 7-7-1945 Electrocuted Harris Huntsville, TX 271 Murder  
 Harris, Curtis 7-1-1993 Lethal Injection Brazos Huntsville, TX 637 Robbery  
 Harris, Danny 7-30-1993 Lethal Injection Brazos Huntsville, TX 649 Robbery  
 Harris, Kenneth 6-3-1997 Lethal Injection Harris Huntsville, TX 901 Rape  
 Harris, T. 5-3-1926 Electrocuted Harris Huntsville, TX 32 Murder  
 Harris, Tommie 6-6-1941 Electrocuted Tarrant Huntsville, TX 235 Murder  
 Hart, Edward Jr. 7-29-1942 Electrocuted Dallas Huntsville, TX 247 Rape  
 Hartfield, William 6-28-1891 Lynched Cass Cass County, TX n/a    
 Haskins, Walter 4-7-1933 Electrocuted Ellis Huntsville, TX 110 Murder  
 Hassell, George J. 2-10-1928 Electrocuted Parmer Huntsville, TX 37 Murder  
 Hawkins, Samuel 2-21-1995 Lethal Injection Lubbock Huntsville, TX 590 Rape  
 Hawkins, William  10-30-1890 Lynched Harris Cypress, TX n/a    
 Hays, Elijah  6-23-1917 Lynched McLennan Reisel, TX n/a    
 Heiselbetz, Jr. Earl 1-12-2000 Lethal Injection Sabine Huntsville, TX 999014 Multiple Murder  
 Helms, Henry 9-5-1929 Electrocuted Eastland Huntsville, TX 70 Robbery  
 Henderson, Ed 6-9-1924 Electrocuted Polk Huntsville, TX 12 Rape  
 Henderson, L. D. 3-21-1947 Electrocuted Grimes Huntsville, TX 286 Murder  
 Henderson, Porter 6-14-1950 Electrocuted Harris Huntsville, TX 329 Murder  
 Henneker, Charles 12-8-1843 Hanged   Galveston Island      
 Henry, Patrick 10-3-1890 Lynched   Nechesville, TX n/a    
 Herman, David 4-2-1997 Lethal Injection Tarrant Huntsville, TX 999003 Robbery  
 Hernandez, Adolph 2-8-2001 Lethal Injection Lubbock Huntsville, TX 978 Murder  
 Hernandez, Ramon 1-30-1987 Lethal Injection El Paso Huntsville, TX 667 Burglary  
 Herrera, Jesus 4-15-1939 Electrocuted Wilson Huntsville, TX 212 Murder  
 Herrera, Leonel 5-12-1993 Lethal Injection Cameron Huntsville, TX 702 Policeman  
 Herrera, Ofilio 6-19-1931 Electrocuted Mason Huntsville, TX 85 Murder  
 Hicks, David 1-20-2000 Lethal Injection Freestone Huntsville, TX 930 Rape  
 Hildreth, W. R. 11-25-1935 Electrocuted Howard Huntsville, TX 157 Murder  
 Hill, Andrew 10-3-1948 Electrocuted Bowie Huntsville, TX 309 Murder  
 Hill, Fred 1-10-1936 Electrocuted Travis Huntsville, TX 162 Murder  
 Hill, Jim 7-3-1896 Hanging Polk Livingston, TX? n/a Murder  
 Hill, Luther 7-5-1942 Electrocuted Panola Huntsville, TX 246 Murder  
 Hill, Mack  Oran 8-8-2001 Lethal Injection Lubbock Huntsville, TX 961 Robbery  
 Holloway, Robert `3-25-1945 Electrocuted McLennan Huntsville, TX 269 Murder  
 Hittle, Daniel 12-6-2000 Lethal Injection Dallas Huntsville, TX 981 Policeman  
 Hogue, Jerry 3-11-1998 Lethal Injection Tarrant Huntsville, TX 660 Robbery  
 Holland, David 8-12-1993 Lethal Injection Jefferson Huntsville, TX 820 Robbery  
 Holmes, Samuel 11-30-1960 Electrocuted Travis Huntsville, TX 418 Rape  
 Hughes, George 5-9-1930 Lynched Grayson Sherman, TX n/a Rape Grayson county farm.
 Hughes, Jr. Billy 1-24-2000 Lethal Injection Matagorda Huntsville, TX 556 Policeman  
 Hulen, R. J. 2-6-1953 Electrocuted Potter Huntsville, TX 367 Murder  
 Humphreys, Harle 5-22-1924 Electrocuted Falls Huntsville, TX 10 Murder  
 Hunt, Dewey R. 12-29-1933 Electrocuted Dallas Huntsville, TX 123 Murder  

Sources:
Texas Department of Criminal Justice Home Page for executions after 1977.  
The Rope, The Chair, And The Needle by James W. Marquart, ©1994, University of Texas Press for those executions before 1977.
Without Sanctuary by James Allen and John Littlefield, © 2000, for early lynchings in Texas.

Killed for being related to John Wesley Hardin.