We simulate the evolution of a dust universe from $$z=1089$$ $z=1089$ to $$z=0$$ $z=0$ by numerically integrating the Einstein’s equation for a spatially flat Friedmann–Lemaire–Robertson–Walker (FLRW) background spacetime with scalar perturbations which are derived from the matter power spectrum produced with the Code for Anisotropies in the Microwave Background (CAMB). To investigate the effects of primordial gravitational waves (GWs) on the inhomogeneity of the universe, we add an additional decaying, divergenceless and traceless primordial tensor perturbation with its initial amplitude being $$3\times 10^{-4}$$ $3\times {10}^{-4}$ to the above metric. We find that this primordial tensor perturbation suppresses the matter power spectrum by about $$0.01\%$$ $0.01\%$ at $$z=0$$ $z=0$ for modes with wave number similar to its. This suppression may be a possible probe of a GWs background in the future.