Dynamic phenomena in electric power systems require fast and accurate algorithms for processing signals. The processing results include synchrophasor parameters, e.g., varying amplitude, phase or frequency of sinusoidal voltage or current signals. This paper presents a novel estimation method of synchrophasor parameters that comply with the requirements of IEEE/IEC standards. The authors analyzed an algorithm for measuring the phasor magnitude by means of a selected artificial neural network (ANN), an algorithm for estimating the phasor phase and frequency that makes use of the zero-crossing method. The original components of the presented approach are: the method of the synchrophasor magnitude estimation by means of a suitably trained and applied radial basic function (RBF); the idea of using two algorithms operating simultaneously to estimate the synchrophasor magnitude, phase and frequency that apply identical calculation methods are different in that the first one filters the input signal using the FIR filter and the second one operates without any filter; and the algorithm calculating corrections of the phase shift between the input and output signal and the algorithm calculating corrections of the magnitude estimation. The error results obtained from the applied algorithms were compared with those of the quadrature filter method and the ones presented in literature, as well as with the permissible values of the errors. In all cases, these results were lower than the permissible values and at least equal to the values found in the literature.