To solve the problem of the lack of modeling and analysis of Advanced Persistent Threat (APT) attacks, an attack-defense game model based on FlipIt with asymmetric information was proposed. Firstly, the assets such as targeted hosts in the network system were abstracted as the target resource nodes and the attack-defense scenarios were described as the alternating control of the target nodes. Then, considering the asymmetry of the feedback information observed by the two sides and the incomplete defensive effect, the conditions of the payoff model and the optimal strategy of the attacker and defender were proposed in the case of renewal defense strategy. Besides, theorems of simultaneous and sequential equilibrium were proposed and demonstrated. Finally, numerical illustrations were given to analyze the factors of equilibrium strategy as well as defense payoff and to compare simultaneous and sequential equilibrium. The experimental results show that period strategy is defender's best strategy and the defender can achieve sequential equilibrium meanwhile obtaining more payoffs compared with simultaneous equilibrium by announcing her defense strategy in advance. Conclusions show that the proposed model can theoretically guide defense strategy towards stealthy APT attacks.