As global temperatures increase, forest fires have increased in frequency and size. The multi-robot system can monitor the fire spread trend in real-time and provide effective information for the global decision-making center. Furthermore, attackers may prevent some robots from making optimal decisions. Therefore, this paper studies the multi-robot cooperative forest fire monitoring problem under cyber attacks, where each robot has the ability to make autonomous decisions. First, the forest fire monitoring problem is considered as a maximum area coverage problem, and the single-step actions of each robot are selected based on the principle of maximizing the submodular function. Based on this, this paper proposes a robust decision-making algorithm that can minimize the attacker's influence on the decision, even in the worst case. Finally, the simulation results verify that the proposed algorithm can achieve maximum forest fire monitoring.