To investigate the effects of complex hysteresis characteristics owing to multi value correspondence and asymmetry on the control accuracy of flexible industrial robot joints, this study proposes a neural network modeling method for complex hysteresis characteristics of asymmetry and strong nonlinearity utilizing the PI (Prandtl Ishlinskii) model framework. Based on the structure of symmetric Play operator in the PI model, the linear part of Play operator is replaced by a new operator that is a nonlinear function constructed by two modified Sigmoid functions with asymmetric nonlinear hysteresis behavior. The new operator is used as the active function that constructs the neural network hysteretic model for capturing the complex hysteresis characteristics of flexible joints. The model is verified using experimental data obtained under different input conditions of flexible joints, and the results show that the maximum prediction error can be controlled within 1°. Compared to the PI model, the maximum error and the root mean square error are reduced to one fifth. Furthermore, it can be proved that the hysteresis neural network has good generalization ability with a modeling accuracy that is greatly improved.