Summary: In this paper, we are concerned with a class of semivectorial bilevel programming problem. Using the optimality conditions of the lower level programs, we construct the corresponding penalized problem. Then, we analyze the relationships between the optimal solution of the original problem and that of the penalized problem, and prove that the penalty function presented is exact. Then, we analyze the optimality conditions for a special semivectorial bilevel programming problem, where the objective functions and constraints functions are all linear functions. Finally, we propose a penalty function algorithm. The numerical results show that the algorithm is feasible to the semivectorial bilevel programming problem considered.