We present a next-to-next-to-leading (fifth or NNLO) order calculation for the covariance matrix of the matter power spectrum, taking into account the effect of survey window functions. Using the grid-based calculation scheme for the standard perturbation theory, GridSPT, we quickly generate multiple realizations of the nonlinear density fields to fifth order in perturbation theory, then estimate the power spectrum and the covariance matrix from the sample. To the end, we have obtained the non-Gaussian covariance originated from the one-loop trispectrum without explicitly computing the trispectrum. By comparing the GridSPT calculations with the N-body results, we show that NNLO GridSPT result reproduces the N-body results on quasilinear scales, where SPT accurately models nonlinear matter power spectrum. Incorporating the survey window function effect to GridSPT is rather straightforward, and the resulting NNLO covariance matrix also matches well with the N-body results.