Asymmetric lineshapes are experimentally observed in the Raman spectra of different classes of condensed matter. Determination of the peak parameters, typically done with symmetric pseudo-Voigt functions, in such situations yields unreliable results. While a wide choice of asymmetric fitting functions is possible, for the function to be practically useful, it should satisfy several criteria: simple analytic form, minimum parameters, description of the symmetric shape as "zero case", estimation of the desired peak parameters in a straightforward way and, above all, adequate description of the experimental data. In this work we formulate the asymmetric pseudo-Voigt function by damped perturbation of the original symmetric shapes with one asymmetry-related parameter. The damped character of the perturbation ensures by construction consistent behavior of the line tails. We test the asymmetric function by fitting the experimental Raman spectra. The results show that the function is able to describe a wide range of experimentally observed asymmetries for different natures of asymmetric broadening, including 3D and 2D crystals, nanoparticles, polymers, and molecular solids and liquids.