The integration of photonic crystal cavity with quantum dot paves the way for photonic-based quantum information processing. Photonic crystal cavity has a high-quality factor and small mode volume, which can be utilized to enhance the interaction between light and matter. Two degenerate fundamental modes with orthogonal polarizations exist in photonic crystal H1 cavity. Entangled photon pairs can be generated with a single quantum dot coupled to degenerate H1 cavity modes. Therefore a coupling system comprised of quantum dot and photonic crystal H1 cavity is a promising platform to implement quantum information processing. The excitations of cavity modes are mostly affected by the location of the single quantum dot, namely a dipole source. For the two degenerate photonic crystal H1 cavity modes, the location of the dipole source determines which mode is excited. In this paper, the effects of location and polarization of a dipole source on the excitation of photonic crystal H1 cavity are investigated with the finite-difference time-domain method, a numerical analysis technique for computing the electrodynamics. We first design a photonic crystal slab structure patterned with hexagonal lattice of air holes. Combining the light modulation by the period lattice in the slab plane and the total internal reflection in the perpendicular direction, photonic bandgap is generated, which inhibits the propagation of photon with certain frequencies. By removing one of the air holes from the photonic crystal slab, an H1 cavity is formed with two degenerate fundamental modes. One mode is x-polarized, and the other one is y-polarized. Next, a dipole source is used to excite the H1 cavity modes. When the dipole source is located at the left to the H1 cavity center, only y-polarized mode is excited. While locating the dipole source above the H1 cavity center, only x-polarized mode is excited. Therefore each degenerate mode of H1 cavity can be selectively excited with the diploe source located at different positions in the cavity. Following that, the H1 cavity modes excited with the dipole sources with different polarizations are also studied. The x-polarized dipole source can only excite the cavity mode with x-polarization, while the y-polarized dipole source can only excite the y-polarized cavity mode accordingly. It can be seen that the dipole source with specific polarization can only excite the modes with corresponding polarization. The effects of location and polarization of a dipole source on the excitation of a photonic crystal H1 cavity are important for understanding the fundamental physics of entangled photon generation with a coupled quantum dot and photonic crystal system.