The 62-year-old victim suffered injuries to her head, thigh, shin, feet and hands following the alleged offence on May Tree Avenue this morning.
She was walking along the road around 10am when a man riding a bicycle came up behind her and grabbed her handbag, Humberside Police said.
As the woman hung on to it, she fell over and was dragged along by the culprit.
She was taken to hospital for treatment.
The man has been described as white, about 30 to 35-years-old, skinny and around 5ft 8ins.
He was wearing a dark blue tracksuit and baseball cap and cycled off towards James Reckitt Avenue.
The cream Radley handbag,a red Biba purse, a Samsung phone, keys and makeup were stolen.
Anyone with information is asked to call 101, quoting reference 16/71383/18.