Recorded Crime in Scotland statistics for 2014/15 also show that violent crime in the city has decreased by 12% between 2013/14 and 2014/15.
The number of homicides has fallen by 3% over the same period.
Justice Secretary Michael Matheson said the figures were "positive" and reflected a wider trend that Scotland was "becoming a safer place".
Mr Matheson said: "Crimes of handling an offensive weapon have dropped dramatically and are now at their lowest level in 29 years.
"We know that knife crime has a devastating impact not only on individuals but family, friends and local communities which is why our preventative approach aimed at educating young people about the potential consequences of carrying a knife is so important.
"The positive statistics in Glasgow mirror the Scotland-wide trend. Our country is becoming a safer place with crime at a 41 year low, violent crime down by over half since 2006/07 and homicides at their lowest levels since records began."
Crimes in Glasgow involving knives and offensive weapons have fallen by 14% in the past year, to a 29 year low.