The parametric array is formed by two finite-amplitude ultrasound beams with neighboring frequencies. The nonlinear interaction of the beams generates a highly directive audible sound at the difference frequency. Up to now, we have analyzed theoretically parametric sound fields in a free space. This study proposes a numerical simulation method of nonlinear ultrasound propagation to estimate the parametric sound field in the time domain. Using the finite-difference time-domain method based on the Yee algorithm with operator splitting, axisymmetric nonlinear propagation was simulated on the basis of equations for a compressible viscous fluid. As model application, a lengthlimited parametric sound beam, which is formed by four finite-amplitude ultrasound beams with different frequencies and controlled by phases and amplitudes of sound sources and has a truncated array length [C.M. Hedberg et al., Acoust. Phys. 56, 637–639 (2010)], was numerically simulated. The simulation showed a spatially restricted and very narrow difference frequency sound beam similar to their experiment. In addition, to investigate the dependence of amplitude and phase on the lengthlimited beam profiles, parametric sound fields were numerically estimated by varying the amplitude and phase slightly from the condition of the length-limited beam. Numerical results indicated that the changes of the amplitude and phase affected the beam length and width, in particular, amplitude changes drastically deformed the beam shape from that of the length-limited beam. This result suggests that precisely controlled sound sources are necessary to obtain the best length-limited sound beam.