By using an unbiased quantum Monte Carlo method, we investigate the hard-core Bose-Hubbard model on a square lattice with anisotropic dipole-dipole interaction. To study the effect of the anisotropy, dipole moments are assumed to be polarized in the y direction on the two-dimensional (2D) xy plane. To perform efficient simulations of long-range interacting systems, we use the worm algorithm with an O(N) Monte Carlo method. We obtain the ground-state phase diagram that includes a superfluid

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... and a striped solid phase at half-filling as two main phases. In addition to these two main phases, we find a small region where there are multi plateaus in the particle density for small hopping amplitudes. In this region, the number of plateaus increases as the system size increases. This indicates the appearance of numerous competing ground states due to frustrated interactions. In our simulations, we find no evidence of a supersolid phase.