A letter sent by the college to its teaching staff at the weekend offers an "incentive" payment of pound;1,800 for those who accept the cut from 48 days to 40.
The letter said: "We believe that 40 days' holiday remains an attractive entitlement in the context of FE colleges generally.
"Information we have on practice in other colleges in the East Midlands shows that most provide between 35 and 40 days of holiday entitlement for their lecturing staff."
But at a packed branch meeting of the lecturers' union Natfhe, on Tuesday, Leicester college lecturers voted unanimously in favour of a strike ballot unless the contract, which comes into effect from August 1, is withdrawn.
The ballot would take place during enrolment week, in September.
In addition, as the new contract automatically applies to new staff, the union is urging members to boycott job vacancies at the college until the dispute is resolved.
Russ Escritt, Natfhe's regional officer, said: "I am appalled that the management at Leicester college are returning to outdated Thatcherite tactics of forcing through contract changes.
"Leicester has, until now, had a fairly good relationship with the union.
But we cannot accept having a new contract being imposed on us that has not been negotiated. If the college does not withdraw this, we will ballot for strike action."
The college has defended the new contract. It says the changes to staff holiday entitlement will create more opportunities for development, training and team building. Marianne Harris-Bridge, the college's director of corporate affairs, also denied the new terms were being imposed.
She said: "A letter was sent out advising staff of the new contract which applies to new staff only.
"Current staff are being given the opportunity to take it up, but we are not imposing it on them. Natfhe was involved in discussions about this at the start but pulled out of negotiations."
Leicester college, which has four campuses, is one of the 10 largest FE institutions in England. Set up in 1999 following the merger of the city's South Fields college and Charles Keene college, it has 26,000 students and around 1,500 staff.