Based on the experiment of austenite SMA wire properties, the influence of strain amplitude on the dynamic properties of SMA wire is studied, and a constitutive model of SMA wire based on a chaotic Gaussian bat (GS-BA) optimized wavelet neural network (GS-BA-WNN) is proposed. In view of such shortcomings as easy early-maturing and low diversity in late period of the basic bat algorithm (BA), the Gaussian disturbance is used to enhance algorithm’s ability to escape local optimum and promote the bat population chaos optimization to improve the population diversity. GS-BA is combined with wavelet neural network to obtain the initial parameter configuration of WNN, and the model of GS-BA-WNN is used to simulate the constitutive relationship of SMA wire under different amplitudes of strain, and at the same time it is compared with the model of WNN and model of WNN (BA-WNN) optimized by BA. The results show that the GS-BA-WNN model established using experimental data as model training data has higher prediction precision and smaller error than other models, and has advantages in predicting the constitutive relationship of SMA wire.