Various elastic wave-based site investigation methods have been used to characterize subsurface ground because the dynamic properties can be correlated with various geotechnical parameters. Although the inherent spatial variability of the geotechnical parameters affects the P-wave propagation characteristics, ground heterogeneity has not been considered as an influential factor. Thus, the effect of heterogeneous ground on the travel-time shift and wavefront characteristics of elastic waves through stochastic numerical analyses is investigated in this study. The effects of the relative correlation lengths and relative propagation distances on the travel-time shift of P-waves considering various intensities of ground heterogeneity were investigated. Heterogeneous ground fields of stiffness (e.g., the coefficient of variation = 10 ~ 40%) were repeatedly realized in numerical finite difference grids using the turning band method. Monte Carlo simulations were undertaken to simulate P-wave propagation in heterogeneous ground using a finite difference method-based numerical approach. The results show that the disturbance of the wavefront becomes more significant with stronger heterogeneity and induces travel-time delays. The relative correlation lengths and propagation distances are systematically related to the travel-time shift.