Based on the measurement noise as the non-Gaussian L´evy noise, a novel Kalman filter for the discrete linear stochastic fractional order system is proposed. By eliminating the maximum, the approximated Gaussian white noise can be obtained. Based on the principle of least square, an improved Kalman filter can be developed for the discrete linear stochastic fractional order system with measurement L´evy noise. Compared to the traditional method, the proposed method gets better performance. Finally, simulation results show the effectiveness and usefulness of the proposed algorithm.