Henry Morgan Dockrell (1880 – 26 October 1955) was an Irish Cumann na nGaedheal and Fine Gael party politician who was elected to both Dáil Éireann and Seanad Éireann.
He was first elected in the 1932 general election as a TD for Dublin County in the 7th Dáil, and was re-elected five times for the same constituency until he was defeated in the 1948 general election.
After the loss of his Dáil seat, Dockrell was elected to the 6th Seanad by the Industrial and Commercial Panel in 1948, but was defeated in the 1951 election for the 7th Seanad.
Dockrell was married (to Alice Evelyn Hayes), and had four sons and one daughter. Two of his sons, H Percy Dockrell and Maurice E. Dockrell were also Fine Gael TDs and councillors. His father, Sir Maurice Dockrell, was a Unionist Member of Parliament.