［Purposes］To study the sufficient optimality conditions for a class of multiobjective semi-infinite programming problems.［Methods］Some new concepts of higher order (B,F)-AC-V-type Ⅰ invex functions are introduced by using the arcwise connected function and the sublinear function. Then a class of multiobjective semi-infinite programming problems including inequality constraints are considered under the new generalized functions. ［Findings］Several sufficient optimality conditions are established. ［Conclusions］The results are of great significance to the multiobjective semi-infinite programming theory.