A product of the youth system at Luton Town, Calvin signed for Crystal Palace in July 2008.

He enjoyed loan spells at Grimsby Town and Bristol City before being given a run in the Luton first team. Whilst at Grimsby, Calvin made eight appearances scoring once but at Bristol he was limited to only three appearances. Calvin made his Luton debut in September 2004 and went on to make a further 11 appearances in that season making 45 appearances for the Hatters overall.

Andrew initially struggled for first team football at Selhurst Park and went out on loan to Brighton & Hove Albion in the second half of his first season at Palace. After scoring three goals in nine appearances including one on his debut, he was forced to return early through injury.

The 2009/10 campaign was Andrew's most productive in a Palace shirt to date. He made a total of 32 appearances in the campaign which saw the Eagles narrowly avoid relegation, scoring twice.

The 2010/11 season saw Calvin make eight appearances for Crystal Palace before going out on loan again to Millwall. The striker only appeared briefly for the Lions before making a further seven appearances for the Eagles in all competitions.

A further loan move to Swindon Town was made towards the end of the 2010/11 season where Calvin made 10 appearances and scored once before returning to Selhurst Park.