The switching of node status on the network is a common natural phenomenon. In this paper, we study the problem of adaptive diffusion strategies with Markov jump. A simple choice for adaptive structures is the Least Mean Square (LMS) filter, which we will improve. The main work of this paper is to introduce Markov transform into diffusion adaptive structure strategies. The main result is that the Adaptive-Combine-Markov (ACM) diffusion strategy and the Combine-Adaptive-Markov (CAM) diffusion strategy are obtained by gradient descent iterative method. Furthermore, a generalized adaptive diffusion strategy based on Markov jump (ADSM) is introduced. Then, we propose several theorems about the average convergence and mean square stability of ADSM, which is enough to prove that our proposed strategies are to promote the existing conclusions. Finally, The simulation experiments also demonstrate the effectiveness of the proposed ADSM.