At present, the most common way for bitcoin mining is miners joining in a pool. However, there is a phenomenon that the mining pools penetrate each other, which will result in a decrease in the miners' income of the attacked pools, and a reduction in computing power of the attacking pools. Therefore, the overall computing power of the bitcoin system is reduced. Aiming at the problem of mutual attack and non-cooperative mining between mining pools, an Adaptive Zero-Determinant strategy (AZD) was proposed to promote the cooperation of miners. The strategy adopted the idea of comparing expected payoff with cooperation and defection in the next round then choosing a strategy with high payoff. Firstly, miners' payoff in the next round under two situations could be predicted by the combination of Temporal Difference Learning Method (TD(λ)) and Zero-Determinant strategy (ZD). Secondly, by comparing the cooperation payoff with defection payoff in the next round, a more favorable strategy was chosen for miners by Decision Making Process (DMP), so the cooperation probability and defection probability in the next round were changed correspondingly. Finally, through the iterative implementation of AZD strategy, the ming pools in the network would cooperate with each other and mine actively. Simulation results show that compared with adaptive strategy, AZD strategy increases the speed of converging cooperation probability to 1 by 36.54%, compared with ZD strategy, it improves the stability by 50%. This result indicates that AZD strategy can effectively promote the cooperation of miners, improve the convergence rate of cooperation and ensure the stable income of mining pools.