A novel completely mode-free integral reinforcement learning (CMFIRL)-based iteration algorithm is proposed in this article to compute the two-player zero-sum games and the Nash equilibrium problems, that is, the optimal control policy pairs, for tidal turbine system based on continuous-time Markov jump linear model with exact transition probability and completely unknown dynamics. First, the tidal turbine system is modeled into Markov jump linear systems, followed by a designed subsystem transformation technique to decouple the jumping modes. Then, a completely mode-free reinforcement learning algorithm is employed to address the game-coupled algebraic Riccati equations without using the information of the system dynamics, in order to reach the Nash equilibrium. The learning algorithm includes one iteration loop by updating the control policy and the disturbance policy simultaneously. Also, the exploration signal is added for motivating the system, and the convergence of the CMFIRL iteration algorithm is rigorously proved. Finally, a simulation example is given to illustrate the effectiveness and applicability of the control design approach.