The problem of opacity has been successfully applied in the field of information security for cyber-physical systems, and recently the attack problem of opacity in discrete event systems has attracted extensive attention of scholars. This paper studies the feasibility of active attacks against infinite-step opacity in the context of supervisory control of discrete event systems. According to whether the attacker can fully attack the secret states in the system, the formal concepts of strong attackability and weak attackability are respectively given. For the closed-loop controlled system with enhanced infinite-step opacity, a new all attack structure model is proposed to record the pre-state and post-state estimations of the attacker and the supervisor, and determines whether the active attacker can complete the attack against infinite-step opacity of the system by tampering with the supervisor's observations without being detected by the supervisor. Based on this model, the necessary and sufficient conditions for strong attackability and weak attackability of infinite-step opacity are respectively deduced. The conclusions and examples demonstrate that the proposed sensor active attack strategy can effectively achieve active attacks against system security.