A multiply sensor faults detection method was proposed for a class of nonlinear system of sensor fault diagnosis problem. First, we defined a state variable to convert the sensor fault as pseudo actuators fault, and then generated the residual through the corresponding sliding-mode observer to realize the fault detection. Based on Lyapunov stability theory, a sufficient condition for observer was derived in the form of linear matrix inequality(LMI). Finally, the correctness and effectiveness of the method were verified through a single link robot simulated experiments.