The staff, members of the lecturers' union Natfhe, say management is trying to force them to perform extra co-ordinating and administrative duties with less time off in which to do them.
In a ballot of 122 members, 78 voted for strike action as a last resort.
Almost all - 108 - favoured industrial action short of a strike. Natfhe membership at City College is around 220.
Adrienne Punt, Natfhe branch secretary, said: "We will not let our employers erode high standards or conditions of service."
Lecturers have since voted overwhelmingly to refuse to undertake extra duties for which previously they had been given free periods, and to work to rule. "Staff at City College are proud of the quality of the education offered to the local community," said Ms Punt.
"It is senior management's belief that by effectively giving lecturers more teaching, they will save money. But courses run poorly because staff are overworked, exhausted and demoralised will cost us our hard-won reputation."
City College principal Dick Palmer said: "We are disappointed that our students are threatened with disruption. Our lecturers have good pay and conditions. We are simply asking them to work to contracted hours."