The digital integrator is one of the important aspects of an electronic current transformer based on an air coil. In this paper, a new extended trapezoidal digital integration algorithm is proposed based on the diagonally implicit Runge-Kutta method. In order to improve the integration accuracy of the new digital integration algorithm, composite integration is used to derive the transfer function of a universal new-type digital integrator at different sample frequencies. Since the transfer function of the new digital integrator contains a fractional delay term, it is simulated using FIR and IIR filter algorithms. The simulation results by Matlab show that the performance of the new digital integrator is better than that of the trapezoidal digital integrator in the low frequency range, which can provide a new design method for the integral part of the electronic current transformer based on Rogowski coil.