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In this paper, a simple method is proposed to evolve artificial neural networks(ANNs) using augmenting weight matrix method(AWMM). ANNs' architecture and connection weights can be evolved simultaneously by AWMM, and their structures incrementally are growing up from minimal structure. It is a non-mating method. It employs 5 mutation operators: add connection, add node, delete connection, delete node, and new initial weight. And the connection weight is trained by the simplified alopex method, which is a correlation based method for solving optimization problem. In AWMM, structural information is encoded to weighting matrix, and the matrix is augmenting as the hidden nodes are added.