All four incidents have taken place since the start of February and saw people having money stolen, with two people being targeted after using an ATM.
The first incident took place on February, 2 at around 2.30pm, when a 77-year-old man was approached on St Nicholas Street after he used an ATM.
The thief reportedly asked him for money then “grabbed” a two-figure sum from him.
The second incident was reported on Friday, February, 5 when a 67-year-old woman had her purse stolen from her bag on Market Street.
The third occurred on Union Street in the centre at around 4.45pm on Sunday, February, 7, when an 80-year-old woman had her purse stolen while she waited at a bus stop.
The fourth crime reported occurred again on St Nicholas Street, it took place at around 11am on Monday February, 8. A 63-year-old woman used an ATM and then went into St Nicholas Centre where she had money stolen right out of her hand.
Sergeant Nick Searle of Queen Street Police Station, said: “I would like to reassure the public that we are carrying out extensive enquiries to trace whoever is responsible for these thefts to trace them as soon as possible.
"Officers are studying a large amount of CCTV footage in connection with this ongoing investigation and we are following a number of lines of enquiry at this time.
“I would also encourage everyone to be extra vigilant when you are taking money from an ATM or out shopping, and to never carry around large quantities of cash.
"Please also keep an eye out for suspicious activity and report any concerns to us.”