It has been challenging for mobile observation platforms to solve the path planning problem in a three-dimensional dynamic marine environment. On the one hand, traditional path planning algorithms are highly dependent on the environment, lack flexibility, and need to be re-modeled and re-planned when the environment changes. On the other hand, traditional algorithms suffer from the problems of difficult modeling, local optimality, and reduced observation efficiency when facing path planning in marine environments. To solve these problems, we introduce 3D ocean information under Princeton Ocean Model (POM) for path planning to improve the robustness of the model to 3D dynamic ocean environment. Then, we enhance the learning ability by combining Recurrent Neural Network (RNN) with Proximal Policy Optimization (PPO) algorithm in order to improve the training efficiency and effectiveness of the algorithm. After training, the observation path of the mobile observation platform can be reasonably planned, forming the three-dimensional dynamic marine environment path planning for the mobile observation platform based on the POM-RNN-PPO algorithm. Simulation results show that the algorithm shows better observation path planning results than other algorithms in three-dimensional dynamic ocean environment, and has good generalization under different sea areas, which provides theoretical and technical support for real mobile observation platform path planning.