During the last decades, Power-law distributions played significant roles in analyzing the topology of scale-free (SF) networks. However, in the observation of degree distributions of practical networks and other unequal distributions such as wealth distribution, we uncover that, instead of monotonic decreasing, there exists a peak at the beginning of most real distributions, which cannot be accurately described by a Power-law. In this paper, in order to break the limitation of the Power-law distribution, we provide detailed derivations of a novel distribution called Subnormal distribution from evolving networks with variable
elements and its concrete statistical properties. Additionally, imulations of fitting the subnormal distribution to the degree distribution of evolving networks, real social network, and
personal wealth distribution are displayed to show the fitness of proposed distribution.