For attack reconstruction issue of cyber–physical systems (CPSs), it is a challenge to guarantee online computational efficiency and reconstruction accuracy simultaneously, especially for cases with actuator attacks. However, most existing approaches are only focused on sensor attacks. This brief paper studies the multiple attack reconstruction problem for CPSs. A new projected intermediate estimator is proposed, where the computation complexity problem is solved by reducing the number of loop iterations significantly via enhancing the designs of loop iteration, termination condition and parameter selection strategy, without sacrificing the attack reconstruction performance. Compared with traditional intermediate estimators, the dependence of linear matrix inequality technique is completely removed, besides, the intrinsic heavy overshooting problem in transient period is effectively alleviated. The application to a networked motion control system verifies the effectiveness and superiority of the presented method.