In this paper, a security problem in remote estimation scenario is studied. We consider a multi-sensor system where each sensor transmits its local innovation to a remote estimator through a wireless communication network. A centralized residue-based detection criterion is adopted to monitor system anomalies. We propose a linear attack strategy and present the corresponding feasibility constraints to guarantee stealthiness. For a resource-limited attacker, who is able to listen to all the channels while only launches an attack on one sensor at each time instant, we investigate which sensor should be attacked and what strategy should be used such that the remote estimation error covariance is maximized A closed-form expression of the optimal linear attack strategy is obtained. Simulation examples are provided to illustrate the theoretical results.