Legged robots have shown great adaptability to various environments. However, conventional walking gaits are insufficient to meet the motion requirements of robots. Therefore, achieving high-speed running for legged robots has become a significant research topic. In this paper, based on the Spring-Loaded Inverted Pendulum (SLIP) model and the optimized Double leg—Spring-Loaded Inverted Pendulum (D-SLIP) model, the running control strategies for the double flying phase Bound gait and the Rotatory gallop gait of quadruped robots are designed. First, the dynamics of the double flying phase Bound gait and Rotatory gallop gait are analyzed. Then, based on the “three-way” control idea of the SLIP model, the running control strategy for the double flying phase Bound gait is designed. Subsequently, the SLIP model is optimized to derive the D-SLIP model with two touchdown legs, and its dynamic characteristics are analyzed. And the D-SLIP model is applied to the running control strategy of the Rotatory gallop gait. Furthermore, joint simulation verification is conducted using Adams virtual prototyping and MATLAB/Simulink control systems for the designed control strategies. Finally, experimental verification is performed for the double flying phase Bound gait running control strategy. The experimental results demonstrate that the quadruped robot can achieve high-speed and stable running.