Abstract: In the global energy transition, hydrogen enriched compressed natural gas is efficiently transported through existing pipelines, increasing the proportion of renewable, low-carbon, and green energy in the energy consumption structure. However, hydrogen source is affected by renewable energy generation for hydrogen production, resulting in fluctuations in the hydrogen blending ratio and posing challenges to the combined cooling, heating, and power system with hydrogen-doped natural gas as the input energy source at the endpoint. Therefore, this article proposes a multi time scale distributed predictive control method for hydrogen doped natural gas electrical hydrogen coupled energy systems. Firstly, an electric-hydrogen coupled cold, heat and power system based on hydrogen-doped natural gas was constructed for exploring the dynamic characteristics of the system during operation. Then, based on the differences in dynamic response characteristics of the system, three subsystems are divided into the electric side, cold side, and hot side to achieve more accurate control. Finally, simulation experiments were conducted to verify that the proposed multi time scale distributed predictive control algorithm can improve the speed of power side tracking while meeting the tracking accuracy of the three types of loads in the system, namely cooling, heating, and power. It can also achieve stable energy supply of the system in scenarios where the hydrogen doping ratio fluctuates.