The design method of fractional-order Kalman filter based on Tustin generating function is proposed to solve the problem on the state estimation for continuous-time linear fractional-order systems with correlated fractional-order colored process noise and fractional-order colored measurement noise. By Tustin generating function method, the continuous-time linear fractional-order system is discretized, the differential equation of fractional-order system is transformed into a difference equation. Using the augmented vector method, the fractional-order state equation and the fractional-order colored noises are constructed as a new augmented state vector, and the fractional-order colored noises are transformed into white Gaussian noises. Then, a fractional-order Kalman filter algorithm based on Tustin generating function is presented to achieve effectively the state estimation of the continuous-time linear fractional-order system involving correlated fractional-order colored process noise and fractional-order colored measurement noise. Compared with Grddotunwald-Letnikov difference, the state estimation obtained by Kalman filter algorithm using Tustin generating function is more accurate and the effect is more satisfactory. Finally, the effectiveness of the proposed algorithms is validated by the simulation result.