A high-quality brazed joint of SiC ceramic and 304 stainless steel (SiC–304SS) was achieved by Cu–10TiH2 brazing alloy. The effects of brazing temperature on the interfacial microstructure and mechanical properties of SiC–304SS were analyzed. The typical interfacial microstructure of joints brazed at 1030 °C for 10 min was 304SS/σ-phase/(Fe, Cr) Ti/Fe2Ti/Cu(s,s) + Fe2Ti + TiC/SiC ceramic. With the brazing temperature increasing, the element Fe continued diffusing into the brazing seam and reacted with the element Ti. Then the width of σ-phase and the amount of Fe2Ti phase became increasing, and Fe2Ti phase became continuous. While, due to the reaction between Fe and Si, a buffer layer formed in SiC–304SS joints brazed at 1040 °C and 1050 °C. The main component of the buffer layer was FeSi2, TiC phases and carbon particles. In addition, the buffer layer contributed to forming a good gradient transition of coefficient of thermal expansion (CTE), releasing residual stress and improving shear strength of the joints. When brazing at 1050 °C for 10 min, the maximum shear strength of the joint was 100 MPa at room temperature and 53 MPa at 600 °C.