To improve the self-heating effect in GaN HEMT, integrating diamond substrate with high thermal conductivity is an effective way for heat dissipation in active region of device. However, columnar grain structures in polycrystalline diamond (PCD) grown by chemical vapor deposition (CVD) cause anisotropic and thickness dependence thermal conductivity of PCD. Therefore, the evolution of diamond grain size during growth was modeled to compute the PCD thermal conductivity along the in-plane and cross-plane directions. Based on the above PCD thermal conductivity model, the limitations of channel temperature in GaN HEMT were derived by computing the analytical model of GaN thermal resistance incorporating the nonlinear thermal conductivity, whose variations were studied with the device structure (gate length, gate width, gate spacing and substrate thickness) and power dissipation. Finally, by comparing with the verified finite element model (FEM) simulation results, two effective thermal conductivities of PCD were extracted, which are 260~310 W/(m·K) and 1 250~1 450 W/(m·K). This calculations provide a fast and effective way to estimate the channel temperature in GaN HEMT on diamond substrate.