In this paper, the partial recursive function is constructed by Hopfield neural networks. The partial recursive function is equivalent with Turing machine, the computability of Hopfield neural networks is therefore equivalent with Turing machine. 本文给出了用Hopfield网计算部分递归函数的构造性证明.由于部分递归函数与图灵机等价,故Hopfield网与图灵机等价。