A man has been charged with using his mobile phone to film up the skirts of teenage girls at a shopping centre in Sydney's inner west.

Police say they were on foot patrol in a Burwood shopping complex on Monday afternoon when they witnessed a man, 53, approach two young women, before placing a mobile phone up their skirts.

After following the man for a short period, officers allegedly saw him use a phone to video under the skirts of two 14-year-old girls.

He was arrested, with an examination of his phone revealing further offences, police allege.

The Croydon man was charged with 13 counts of filming a person's private parts, one of attempting the same and two counts of possessing cannabis.

He was allowed bail and will appear in Burwood Local Court on February 14.