This study proposes a numerical simulation method that predicts nonlinear propagation of ultrasound beams in order to estimate the sound field of parametric array in the time domain. Basically, the method resorts to solving numerically and compactly the governing equations in a compressible viscous fluid using the Yee algorithm finite-difference time domain method. The simulation indicates a narrow audible sound beam which is a feature of the parametric array. Additionally, a length-limited parametric sound beam, which is proposed by Hedberg et al. [C. M. Hedberg et al., Acoust. Phys. 56, 637-639 (2010)], is numerically simulated as a model application. A pair of parametric sound sources generates the length-limited sound beam by control of the amplitudes and initial phases of the sources. The simulation shows a narrow truncated array length-limited sound beam.