The council will make the cuts over the next two years and has blamed reduced government funding and a growing demand for its services for the budget shortfall.
A spokeswoman for the council told Personnel Today that it was too early to say which specific jobs would go, but she could not rule out HR jobs being lost.
Pete Bungard, chief executive of the council, said: "It's no secret that the council is facing a tough challenge over the next few years. We are absolutely committed to improving our front-line services and, in order to do that, we have to make some big changes as an organisation.
"While we are looking at lots of ways to save non-staff costs, with the scale of savings needed, there will inevitably be a reduction in jobs as part of the overall approach."
But Ian Ducat, South West regional secretary of the public sector union Unison, said the £60m shortfall could potentially lead to 2,000 jobs being lost in both the public and private sectors in the region.
"There are of course many questions to be answered, not least of which is the apparent contradiction of central government allocating £1bn to local authorities across the country (through the Futures Job Fund) to save jobs while councils are planning to cut spending and make staff redundant.
"A cut of £60m is potentially a loss of 2,000 jobs to the Gloucestershire economy, and that's bad news for everyone in the private and public sector - this cannot be what the government intended."