The research of reinforcement learning-based motion control has progressed significantly for the bipedal and quadrupedal robots. However, the deep reinforcement learning control of octopod robots is still in the exploratory stage due to the issues such as high degrees of freedom redundancy, easy interference at the foot end, and complex dynamic modeling. To address this problem, this paper proposes a motion control framework of crab-like octopod robots based on the deep reinforcement learning. Firstly,, the mechanism model and reference gait of the crab-like robot are designed by analyzing the body structure and gait of crabs, which provides the physical prior knowledge for reinforcement learning. Subsequently, an end-to-end deep reinforcement learning training framework is designed to imitate the reference actions of crab gaits, where a behavior cloning initialization strategy is introduced to accelerate the convergence of the policy. At the same time, a phased reinforcement learning method is adopted to gradually increase the terrain difficulty, ensuring that the robot can stably transfer from the flat ground gait to complex terrains. This paper further compares and analyzes different learning rate adjustment strategies as well as the adaptability of the proximal policy optimization (PPO) algorithm with actor-critic (A2C), soft actor critic (SAC), and deep deterministic policy gradient (DDPG) algorithms. Additionally the generalization ability of model under the dynamic disturbances and diverse terrains through domain randomization training and behavior cloning + staged reinforcement learning methods is studied. The simulation experiment results show that the proposed framework outperforms other algorithms in training efficiency, with the gait stability index( i.e., the standard deviation of the five-step center of mass height) of approximately 0.004 m. The robot can achieve the stable movement on complex terrains such as slopes and steps, whose motion performance is superior to that of the trained model. Finally, a preliminary prototype experiment was conducted to verify the feasibility and stability of proposed method in a real physical environment. In conclusion, the proposed deep reinforcement learning framework combing the biological gait imitation, behavior cloning initialization and phased reinforcement learning provides a new technical approach for the motion control of octopod robots.