The investigation of the III-V nitride-based driving circuits is in demand for the development of GaN-based power electronic devices. In this work, we aim to grow high-quality InGaN/GaN heterojunctions on the n-channel AlGaN/GaN-on-Si high electron mobility transistor (HEMT) templates to pursue the complementary p-channel conductivity to realize the monolithic integrated circuits. As the initial step, the epitaxial growth is optimized and the structure properties are investigated by comparing with the InGaN/GaN heterojunctions grown on GaN/sapphire templates. It is found that both the In composition and relaxation degree are higher for the InGaN/GaN on the HEMT template than that on the sapphire substrate. The crystalline quality is deteriorated for the InGaN grown on the HEMT template, which is attributed to the poor-quality GaN channel in the HEMT template. Further analysis indicates that the higher In incorporation in the InGaN layer on the HEMT template may be caused by the higher relaxation degree due to the compositional pulling effect. An increase in the growth temperature by 20 °C with optimized growth condition improves the crystalline quality of the InGaN, which is comparable to that on GaN/sapphire even if it is grown on a poor-quality GaN channel.