In order to describe the network evolving features for Cognitive Radio Ad Hoc Networks (CRAHNs) and improve the network performance, an evolving network model with preference and anti-preference based on complex network theory is proposed.The aim of the evolving model is to optimize network structures considering the limited node energy, time and location varying spectrum availability and users behaviors in CRAHNs.It is analysed by the mean field theory and proved that the network produced by our model has the scale-free property.The analysis results show that the network is accorded with the scale-free network.This evolving model can improve the scale-free property in degree correlation, clustering coefficient and average path length with node energy and spectrum heterogeneity.Numerical simulation results indicate that the evolving network model has superior performance in balancing the consumption of node energy and spectrum resource between connectivity,so that prolong the network lifetime and develop the network transitivity, which are affected by the node failure due to node energy depletion and the link interruption due to the activity of primary users on licensed spectrum bands.From the analysis and numerical simulation results, the evolving network model is proved an available approach for establishing and analyzing the real CRAHNs.