In this paper, we propose a star-like weakly connected memristive neural network which is organized in such a way that each cell only interacts with the central cells. By using the describing function method and Malkin’s theorem the phase deviation of this dynamical network is obtained. And then, under the Hebbian learning rule the phase deviation is designed as a desired model for associative memory. Moreover, we take the store and recall of digital images as an example to demonstrate the performance of associative memory. The main contribution of this paper is supply a useful mechanism which the new potential circuit element memristor can be used to realize the associative.