Smart grid, equipped with modern communication infrastructures, is subject to possible cyber attacks. Particularly, false report attacks which replace the sensor reports with fraud ones may cause the instability of the whole power grid or even result in a large area blackout. In this paper, a trustiness system is introduced to the controller, who computes the trustiness of different sensors by comparing its prediction, obtained from Kalman filtering, on the system state with the reports from sensor. The trustiness mechanism is discussed and analyzed for the Linear Quadratic Regulation (LQR) controller. Numerical simulations show that the trustiness system can effectively combat the cyber attacks to smart grid.