We have measured the probability distribution function (PDF) of a cosmic matter density field from a suite of N-body simulations. We propose the generalized normal distribution of version 2 ( ) as an alternative fitting formula to the well-known log-normal distribution. We find that provides a significantly better fit than that of the log-normal distribution for all smoothing radii (2, 5, 10, 25 Mpc h−1) that we studied. The improvement is substantial in the underdense regions. The development of non-Gaussianities in the cosmic matter density field is captured by continuous evolution of the skewness and shift parameters of the distribution. We present the redshift evolution of these parameters for aforementioned smoothing radii and various background cosmology models. All the PDFs measured from large and high-resolution N-body simulations that we use in this study can be obtained from the web site https://astro.kias.re.kr/jhshin.