The aim of this paper is to introduce and study upper and lower almost $\gamma$-continuous multifunctions as a generalization of some types of continuous multifunctions including almost continuity, almost $\alpha$-continuity, almost precontinuity, almost quasi-continuity and $\gamma$-continuity. Furthermore, basic characterizations, preservation theorems and several properties concerning upper and lower almost $\gamma$-continuous multifunctions are investigated. The relationships between almost $\gamma$-continuous multifunctions and the other types of continuity are also discussed.