Exchange coupling between topological insulator and ferromagnetic insulator through proximity effect is strongly attractive for both fundamental physics and technological applications. Here we report a comprehensive investigation on the growth behaviors of prototype topological insulator Bi2Se3 thin film on a single-crystalline LaCoO3 thin film on SrTiO3 substrate, which is a strain-induced ferromagnetic insulator. Different from the growth on other substrates, the Bi2Se3 films with highest quality on LaCoO3 favor a relatively low substrate temperature during growth. As a result, an inverse dependence of carrier mobility with the substrate temperature is found. Moreover, the magnetoresistance and coherence length of weak antilocalization also have a similar inverse dependence with the substrate temperature, as revealed by the magnetotransport measurements. Our experiments elucidate the special behaviors in Bi2Se3/LaCoO3 heterostructures, which provide a good platform for exploring related novel quantum phenomena, and are inspiring for device applications.