The attacks, including groping offences, have been recorded in busy areas of the city that are popular with shoppers and people enjoying a night out at bars, restaurants and clubs.
Many such attacks are carried out by assailants unknown to their accuser and include women being touched by men walking past them on the street.
Rape Crisis Scotland has said it is concerned by the rise, and warned those who get away with these offences can go on to commit more extreme crimes.
Chief Superintendent Val Thomson of Strathclyde Police, who is responsible for policing the city centre, said: "We have seen a rise in indecent assaults by strangers within the city.
"By that I mean women walking down the street and being touched on the breast or bottom by somebody walking past."
The number of indecency crimes – not including those related to prostitution – rose 48% to 192 in 2011-12 in the centre of Glasgow, the area hemmed by the M8 motorway to the north and west, the Clyde to the south and High Street and Saltmarket to the east.
The overall level of sex crime across the whole city rose by 16%, from 904 in 2010-11 to 1055 in 2011-12.
National statistics released this summer also showed sex crime figures bucking overall trends of falling criminality.
Ms Thomson said police are still trying to figure who was behind the spate of sleaze attacks, stereotypically associated with southern Europe. But they are not jumping to conclusions about the nationalities of perpetrators.
Ms Thomson said: "We are looking at the profile of the offenders involved in that because it is not something we've experienced before.
"Or is this something women have experienced before but have not reported to us before? We need to get a better understanding of this."
Historical abuse cases, internet child pornography and other trends are also driving up headline sex crime figures.
The force has announced plans for a new unit to help push up convictions for rape and serious sex assaults, with special female advocates to help victims.
On the indecent assault cases, Sandy Brindley of Rape Crisis Scotland said: "Although it can be seen by some as 'minor' crimes, experiences such as having your breast groped can have a significant impact.
"It is crucial the justice system is able to respond swiftly and effectively to these crimes. There is evidence that people who commit these types of crimes can escalate their behaviour."
Figures for sex crime in the city centre were calculated by our sister paper, The Evening Times, which has been crunching police beat crime data for the last six years. The figures are the highest since the paper began the project.
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