The effective set method plays a crucial role in practical applications due to its inherent safety and reliability. This paper proposes an effective set method for solving multi-objective programming problems with linear constraints. This method generates feasible directions through a special linear programming problem that is easy to solve and generates step sizes through an exact line search problem with an explicit solution. Under relatively weak conditions, this paper proves that the sequence generated by the above algorithm converges to a Karush-Kuhn-Tucker stable point of the original problem, and under the assumption of convexity, it is proved that the accumulation point of this algorithm is a weakly efficient solution to the original problem. Finally, the effectiveness and superiority of the algorithm in solving multi-objective optimization problems are verified through numerical experiments.