We address the issue of intra-channel nonlinear compensation using a Volterra series nonlinear equalizer based on an analytical closed-form solution for the 3rd order Volterra kernel in frequency-domain. The performance of the method is investigated through numerical simulations for a single-channel optical system using a 20 Gbaud NRZ-QPSK test signal propagated over 1600 km of both standard single-mode fiber and non-zero dispersion shifted fiber. We carry on performance and computational effort comparisons with the well-known backward propagation split-step Fourier (BP-SSF) method. The alias-free frequency-domain implementation of the Volterra series nonlinear equalizer makes it an attractive approach to work at low sampling rates, enabling to surpass the maximum performance of BP-SSF at 2× oversampling. Linear and nonlinear equalization can be treated independently, providing more flexibility to the equalization subsystem. The parallel structure of the algorithm is also a key advantage in terms of real-time implementation.