The definition region of Zadeh fuzzy operator is extended and the max-min operator is redefined such that it satisfies the exchange law, the combination law and the 0-element law. On the above basis, a max-min operator neural network is proposed according with the general definition of fuzzy operator neural networks. Comparing with traditional fuzzy Zadeh operator neural networks, the present network has high mapping ability. It is showed in detail that the max-min operator neural network can compute part-recursion function, which is equivalent to Turing machine. This indicates that fuzzy max-min operator neural network has the same computation ability as Turing machine. This extends the result of Turing equivalence of traditional neural networks of neuron M-P model to fuzzy neural networks.