Two neural networks with randomly chosen initial weights may achieve the same weight vectors in the process of their mutual learning. This phenomenon is called a network synchronization, and can be used in cryptography to establish the keys for further communication. The time required to achieve consistent weights of networks depends on the initial similarity and on the size of the network. In the previous work related to this topic the weights in TPM networks are randomly chosen and no detailed research on used distribution is performed. This paper compares the synchronization time obtained for the network weights randomly chosen from either the uniform distribution or from the Gaussian distribution with different values of standard deviation. The synchronization time of the network is examined here as a function of different numbers of inputs and of various weights belonging to the intervals with varying sizes. The standard deviation of Gaussian distribution is selected depending on this interval size in order to compare networks with different weights intervals, which also constitutes a new approach for selecting the distribution’s parameters. The results of all analyzed networks are shown as a percentage of the synchronization time of a network with weights drawn from uniform distribution. The weights drawn from the Gaussian distribution with decreasing standard deviation have shorter synchronization time especially for a relatively small network.