The Alliance says the grant should be subject to the couple attending three marriage training sessions.
Leader Sidney Cordle said: "We are very concerned about marriage and the breakdown of marriage in particular.
"Government figures have shown this is costing the nation £47 billion a year," he added.
Mr Cordle was speaking at the launch event in Westminster. His party is putting up 17 candidates in seats across the UK.
Other key pledges outlined include:
"We are very concerned about abortion," said Mr Cordle. "There are 185,000 abortions taking place per year in this country and recently in Parliament they debated gender-selective abortions, people being aborted just because they were the wrong sex. Parliament decided they weren't going to stop it. We think that is outrageous."
In February, MPs agreed to review the extent to which abortion on grounds of gender alone - which is illegal - was being carried out in the UK. However, Health Select Committee chairwoman Dr Sarah Wollaston told the Commons there was no evidence of a "systematic practice" of sex selective abortion in the UK.
According to Mr Cordle, other parties were failing to address several important issues. "I believe marriage, abortion and the persecution of Christians are extremely important and they should be discussed," he said.
The Christian People's Alliance has contested seats in local council and European elections before. In the 2009 European Elections, it ran a combined list with the Christian Party and gained 249, 493 votes or 1.65% of those cast. The parties have agreed not to stand against each other on 7 May.
Mr Cordle hit the headlines in May last year when he told the BBC that storms could have been the result of God's anger at gay marriage legislation. He was being interviewed after UKIP expelled a local councillor for blaming the storms on gay marriage.
"A lot of Christians believe that God is angry over gay marriage and God can actually show that anger," he said.
Asked if his party would welcome votes from gay people, he said: "We don't judge people because of their lifestyle. We are not against people. It's the principles on which we stand."
The Christian People's Alliance has launched its manifesto, calling for a £10,000 grant to all couples on their first marriage.