In this paper, we present a new approach which is spanning tree-based genetic algorithm for solving a multi-objective transportation problem. The transportation problem as a special type of the network optimization problems has the special data structure in solution characterized as a transportation graph. In encoding transportation problem, we introduce one of node encodings based on a spanning tree which is adopted as it is capable of equally and uniquely representing all possible basic solutions. The crossover and mutation were designed based on this encoding. Also we designed the criterion that chromosome has always feasibility converted to a transportation tree. In the evolutionary process, the mixed strategy with (µ+λ)-selection and roulette wheel selection is used. Numerical experiments show the effectiveness and efficiency of the proposed algorithm.