Backscatter wireless communication is an emerging technique widely used in passive radio frequency identification (RFID) systems. Recently, the requirement of a high data rate, data reliability, and secure transmission is becoming the main driving force for the development of RFID systems, which motivates the introduction of multiple-input multiple-output (MIMO) schemes and physical layer security techniques into backscatter systems. In this paper, the combination of multiple antennas and physical layer security techniques is exploited to improve the security level of backscatter systems. We propose a noise-injection precoding strategy and subsequently study the transmit optimization, wherein we aim at maximizing the achievable secrecy rate (SRM) under a total transmit power constraint. To this end, the sequential parametric convex approximation (SPCA) method is exploited to tackle the non-convex SRM problem and subsequently an algorithm based on projected gradient (PG) is proposed for fast implementation, which is especially beneficial to the resource-constrained RFID device. Our simulation results show the superior secrecy rate performance achieved by the proposed noise-injection precoding scheme and high computational efficiency of the proposed fast PG algorithm.