The upcoming generation of galaxy surveys will probe the distribution of matter in the universe with unprecedented accuracy. Measurements of the matter power spectrum at different scales and redshifts will provide stringent constraints on the cosmological parameters. However , on non-linear scales this will require an accurate evaluation of the covariance matrix. Here, we compute the covariance matrix of the 3D matter density power spectrum for the concordance ΛCDM cosmology from an ensemble of N-body simulations of the Dark Energy Universe Simulation-Parallel Universe Runs (DEUS-PUR). This consists of 12288 realisa-tions of a (656 h −1 Mpc) 3 simulation box with 256 3 particles. We combine this set with an auxiliary sample of 96 simulations of the same volume with 1024 3 particles. We find N-body mass resolution effect to be an important source of systematic errors on the covariance at high redshift and small intermediate scales. We correct for this effect by introducing an empirical statistical method which provide an accurate determination of the covariance matrix over a wide range of scales including the Baryon Oscillations interval. Contrary to previous studies that used smaller N-body ensembles, we find the power spectrum distribution to significantly deviate from expectations of a Gaussian random density field at k 0.25 h Mpc −1 and z < 0.5. This suggests that in the case of finite volume surveys an unbiased estimate of the ensemble averaged band power at these scales and redshifts may require a careful assessment of non-Gaussian errors more than previously considered.