He made the comments after he was told he would not get a new parish when he leaves his existing one in London.
The Reverend Andrew Foreshew-Cain is leaving his congregation in West Hampstead as he is moving to the Peak District with his husband.
He said he felt under constant pressure being a gay man working in the Church.
Speaking to BBC Radio 5 live's Stephen Nolan, he said: "The people of the Church of England, the worshipping congregations up and down the country are amazing people who worship and serve their local communities and do tremendous amounts of good in lots of places and for the most part they are welcoming and accepting of the LGBTI community.
"The problem is with the leadership of the Church which maintains and promotes policies and practices which are discriminatory against LGBTI people."
He added: "There's this constant pressure of being a gay man working for the Church of England, in an institution which is institutionally homophobic and has policies and attitudes towards the LGBT community which are harmful."
Father Foreshew-Cain has been a vicar for 27 years and is the vicar of St Mary with All Souls, Kilburn, and St James in West Hampstead.
He has told his congregation he plans to leave in July as his husband is now working 200 miles away.
He said after he married in 2014, he received a letter from his bishop saying he would not be allowed to work in another job within the Church.
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