In this paper, we propose a genetic algorithm(GA) based locomotion method of a quadruped robot with waist joint, which makes a quadruped robot walk on the slop efficiently. In the proposed method, we first derive the kinematic model of a quadruped robot with waist joint and then set the gene and the fitness function for GA. In addition, we determine the best attitude for a quadruped robot and the landing point of a foot in the walk space, which has the optimal energy stability margin(ESM). Finally, we verify the effectiveness of the proposed method by comparing with the performance of the previous method through the computer simulations.