Gallium nitride (GaN)-based P-channel (Pch) and N-channel (Nch) metal-oxide-semiconductor field-effect transistors (MOSFETs) with normally off operations were realised. Both Pch and Nch MOSFETs were monolithically fabricated in a polarisation-junction platform wafer. The platform wafer was constructed with a GaN/aluminium GaN/GaN double heterostructure, which has both two-dimensional hole gas (2DHG) and 2D electron gas (2DEG). The drain currents of Pch and Nch MOSFETs flow through 2DHG and 2DEG, respectively. The threshold gate voltages of the fabricated Pch and Nch MOSFETs were -2.7 and 6.7 V, respectively. It was shown that the threshold voltage and the on-state resistance of the Pch MOSFET can be controlled by adjusting the 2DEG potential. Furthermore, using Pch and Nch MOSFETs, complementary MOS inverter operation was demonstrated.