Closed circuit television has captured footage of a man "grabbing" at female pedestrians in the CBD, in a series of incidents described as "bizarre" by police.

Investigators said the man continually darted amongst people walking along Swanston Street, near Flinders Lane and outside St Paul’s Cathedral, at about 5.30pm last Wednesday.

In the footage released to the public the man is pictured chasing a woman out onto Swanston Street, appearing to grab at her arm or handbag.

He then returns to a park bench near St Paul’s Cathedral where he watches the passing traffic.