In a terahertz (THz) band, a graphene- based patch antenna is widely used due to its unique characteristics. In this paper, a high gain 1 x 2 microstrip patch antenna array based on periodic and non-periodic photonic crystals with a graphene load is proposed to operate in the terahertz band, which has applications in sensing, imaging and wireless communication technologies. First, the properties of graphene were analyzed by varying the chemical potential (mu(c)) from 0 to 1.5 eV. Next, the performance of the proposed antenna array based on periodic photonic crystals with a graphene load is compared to the case with no graphene load. The best performance was achieved at a resonant frequency of 0.630 THz when chemical potential (mu(c)) is 1.5 eV, which achieved a minimal return loss of - 73.86 dB, a bandwidth of 287 GHz, a gain of 11.11 dB and directivity of 12 dBi. In addition, we described three different enhancements to the photonic crystal substrate by designing three different antenna arrays with different air holes in square and triangular lattices. The simulation results indicated that performance improved further with non-periodic photonic crystals as found in antenna array 3 which obtained a minimal return loss of - 75.90 dB and larger bandwidth greater than 411 GHz at a resonant frequency of 0.636 THz. The achieved gain and directivity were 11.53 dB and 12.40 dBi, respectively. The simulation is performed with the aid of CST microwave studio.