Energy efficiency has been the focus of the quadruped robots since the appearance of this field. Most approaches have focused on the quadrupedal mechanisms or the actuation like series elastic actuation (SEA). This work aims to develop an optimal energy efficiency method to plan a quasi-elliptic motion trajectory for the quadruped robots. The energy efficiency of the DC motors in the electric quadruped robot is formulated as an optimization problem. The Stochastic Linear Complementarity Problem (SLCP) and sinusoidal pulse force are proposed to minimize the energy loss at the impact collisions. The stability and energy efficiency of the proposed algorithm is verified with the computer simulation.