Applying EKF(extended Kalman filter) based integrated navigation to correct the measurement error of MEMS（Micro-electromechanical Systems）suffers great computational load, slow convergence and implementation infeasibility. Based on steepest decent algorithm and complementary filter theory, this paper presents an attitude error correction method using MARG (Magnetic, Angular Rate, and Gravity) sensor array. This method uses the Jacobian matrix to substitute the recurrence formula of EKF, which significantly reduces the computational complexity. It only requires to tune two filter gains which are determined by the gyroscope measurement error leading to an ease of implementation. The experimental results of MARG/EKF simulation and MARG/turntable indicate that our proposed method has lower computational complexity and faster convergence than the EKF method. In addition, our proposed method can achieve high accuracy when MARG sensors are operated at low sampling rates, which is very desirable for applications constrained by low power consumption or limited processing resources.