The power grid is a kind of national critical infrastructure directly affiliated to human daily life. Because of the vital functions and potentially significant losses, the power grid becomes an excellent target for many malicious attacks. Due to the special nonlinear measurements, many detection methods do not match the grid very well. The extended Kalman filter based detection is one of the few methods suitable for nonlinear system detection, and therefore can be used in power system to spot malicious attacks. However, the reliability and effectiveness of the extended Kalman filter based detection have not been fully studied and adequately guaranteed. By proposing a two-step false data injection attack strategy, this paper gives a stealthy way to inject false data of increasing magnitude into the power grid, which can eventually cause a certain degree of deviation of the grid state without being detected. In the simulation, the method proposed in this paper caused a voltage deviation of more than 25% before being discovered in the power system.