The Lib Dems gained three seats in last week's election, but had a hard campaign marred by repeated spats over Tim Farron's views on homosexuality.
Lord Paddick, who had been home affairs spokesman throughout the election campaign, announced on Twitter that he was resigning "over concerns about the leader's views on various issues" that came to the fore in the run-up to the election.
The Liberal Democrats managed just 12 seats on June 8, despite uncertainty in a post-Brexit Britain.
But their fortunes have fallen since, as they swooned from 57 seats to eight in the 2015 voting. Farron's majority was slashed from more than 9,000 to about 700 votes. During the run-up to the election, Farron was robustly questioned about his views on gay sex and whether it is a sin, something that he had admitted earlier in his career.
His past comments on abortion were another subject of scrutiny, after a 2007 interview emerged in which he said abortion was "wrong".
The BBC's chief political correspondent Vicki Young said Mr Farron had spoken at length at the "personal quandary" he found himself in and how he felt questions about his faith had "distracted" from the party's efforts during the election.
After the matter refused to go away and surfaced again during the election campaign, Mr Farron said it had felt "impossible" to be both Lib Dem leader and a Christian.
Farron said that his decision to step down was voluntary and he retained the support of the party.
Explaining the move, he stated it was an opportunity to give the party "another powerful voice" following an increase in the number of MPs.
The Liberal Democrats have as strong a record as any party on gay rights, and Mr Farron insists he is passionate about defending the rights and liberties of people who believe differently to him.