The evolving rule includes random attachment and preferential attachment and so on. It forms different network formation by different attachment. In order to analyze this character, this paper put forward an evolving model. It contains two kinds of attachment: some are connected at random, and others are connected based on current structure of the network, and in the model the deleted links are considered. The degree distribution and degree exponent are obtained by mean-field approach. Then it discusses the influence of randomness on the average path length.