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In this article, a novel method is proposed to solve the adaptive optimal tracking algorithm for a class of Markov jump systems. First, the augmented system with the tracking signal is built under the decoupling Markov jump systems and it is proved that the selected performance index satisfies the algebraic Riccati equation which can be solved by policy iteration schemes. Then, a reinforcement learning (RL) algorithm is used to solve the coupled algebraic Riccati equations by using partial knowledge of system dynamics. The convergence of the partial model-free integral RL iteration algorithm is also proved. Finally, a simulation example is given to show the better tracking effectiveness and accuracy of the online iteration algorithm comparing with the offline one.

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