All three incidents occurred in the early evening between 5pm and 8pm in the Flaxley Road area. The incidents were reported at the end of January, mid-February and the last one on 1 March.
The man approached the women and tried to touch them through their clothing. On each occasion, the women hit back and the man ran off. None of the women were physically injured.
The man is described as white, aged between 19 and 25, around 6ft tall, of big build and wearing dark clothing with a hood pulled over his head.
Police are appealing for anyone with any information or anyone who may have witnessed the incidents to come forward.
They are also appealing to any other women who believe they may have been a victim of the man to contact police.
Anyone with information is asked to contact DC Hoban at York CID on 0845 60 60 247.

