New Hampshire increased from 3 seats to 4 seats after the 1790 census.
| District | Incumbent | Party | First elected | Result | Candidates | |
|---|---|---|---|---|---|---|
| Jeremiah Smith | Pro-Administration | 1790 | Incumbent re-elected. | √ Jeremiah Smith (Pro-Admin) 24.1% √ Nicholas Gilman (Pro-Admin) 16.3% √ John Samuel Sherburne (Anti-Admin) 14.2% √ Paine Wingate (Pro-Admin) 12.2% Abiel Foster (Pro-Admin) 8.9% James Sheafe (Pro-Admin) 8.2% Nathaniel Peabody 7.7% Timothy Walker 4.0% William Page 2.3% Joshua Atherton 2.3% | ||
| Samuel Livermore | Pro-Administration | 1789 | Retired Anti-Administration gain. | |||
| Nicholas Gilman | Pro-Administration | 1789 | Incumbent re-elected. | |||
| None (Seat created) | New seat. New member elected. Pro-Administration gain. | |||||