Multi-objective optimization problems are very important, but it is hard to optimized or solved. Generalized ant colony optimization (GACO) algorithm is a new kind of ant colony optimization (ACO) algorithm developed in recent years. In this paper, we try to combine Multi-objective optimization problems with GACO algorithm, established a model for multi-objective GACO algorithm by absorbing state Markov chain, and present a method for estimating the convergence speed of multi-objective GACO algorithm. Simulation results show that the convergence speed of multi-objective GACO algorithm is faster than traditional multi-objective ACO algorithm.