Abstract: This paper presents a direct numerical simulation of an isotropic decaying turbulence. The instantaneous characteristics of the decaying turbulence are obtained. The energy distributions are studied on different spherical surfaces with wave number as radius in spectral space. The results show that both values taken by kinetic energy and enstrophy have certain ranges at each wave number. They cover several orders of magnitude at most of wave numbers. The wave numbers also have wide ranges at each value of kinetic energy or enstrophy. The probability density functions (PDF) for kinetic energy and enstrophy share the same distribution at the same non-dimensional wave number. They exhibit almost no changes along with the decay of turbulence. The PDFs for the enstrophy nearly have the same distribution at different wave numbers when the length scales are far away from the Kolmogorov scale. When the length scales gradually approach to the Kolmogorov scale, the peak value of the PDF increases and moves to the low enstrophy region. The values of the PDF decrease in the high enstrophy region.