The incident happened at 7:19 p.m. on Thursday, November 8th at the Food Lion supermarket in the Beaver Brook Plaza.
Police say the 48-year-old woman was pushing a shopping cart into the store when she felt a tug on her arm.
She turned around to see a man trying to take her purse.
A surveillance image released by police shows the woman hanging on to the purse as the suspect tries, and ultimately fails, to take it away.
The woman fell to the ground and the suspect ran off. She was not injured.
Anyone with information is asked to contact the Robbery Unit at Troop 2 at 302-834-2630 extension #6, or Delaware Crime Stoppers at 1-800-TIP-3333. Information may also be provided at www.tipsubmit.com. You can also send an anonymous tip by text to 274637 (CRIMES) using the keyword "DSP."