In this paper a new subset of the time-invariant microstatistic filters so-called microstatistic Volterra filters are proposed. This class of nonlinear filters is based on the idea of the conventional microstatistic filter generalization by substituting Wiener filters applied in the conventional microstatistic filter structure by Volterra filters. The advantage of the microstatistic Volterra filters in comparison with the Wiener filters, Volterra filters and conventional microstatistic filters is the fact that in the case of non-Gaussian signal processing the microstatistic Volterra filters can outperform Wiener filters, Volterra filters or conventional microstatistic filters. The validity of this basic property of the microstatistic Volterra filters is verified by a number of computer experiments. The disadvantage of the microstatistic Volterra filters is their relatively high computational complexity.