We get a new operator based on the integral principle of the Tustin integral operator with changing the sampling interval of the Tustin integral operator to improve the integral accuracy. Then we design the new operator through the FIR fractional delay filter, and Continuous Fractional Expansion (CFE) is used to realize the new digital fractional order integrator. Examples demonstrated that the performance of new digital fractional order integrator is better than conventional digital fractional order integr...