Hundige Kirke is one of the two churches in the parish of Hundige-Kildebrønde and is also the most recent. The architect gained inspiration for the actual church building from the reconstructed buildings in the Trelleborg Viking Fortress.
During the 1960s and 1970s, the Køge Bugt area and therefore also Greve saw a population explosion, and churchgoers and church authorities soon realised that the old, beautiful village churches in the area would not be able to properly serve the thousands of people.
The church, which also houses a church centre, was designed by the architect Ejvind Draiby. Construction started in February 1975, and the church was inaugurated in October 1976.