Abstract: Directivity is a direct indicator of the audio sound generated by parametric array loudspeakers. However, due to the complex nonlinear process involved, predicting directivity accurately and efficiently is difficult. The far-field directivity of a rectangular parametric array loudspeaker is deduced theoretically based on the direct and the modified spherical convolution models in this paper. The effect of the audio frequency on directivity of a rectangular piston source parametric array loudspeaker with half length of 0.2 m and source frequency of 64 kHz is investigated by numerical simulations, and it is verified by experimental measurements in an anechoic chamber. The results indicate that the modified spherical convolution model provides better prediction results in the main lobe, and can predict sidelobe components at high audio frequencies. Currently, the modified spherical convolution model is one of the most effective and accurate prediction methods for directivity.