Ultra-high performance concrete (UHPC) is widely used in retrofitting damaged structures, but few studies on the strengthening of stone arch bridges have been reported. This paper presents a simplified analysis method and its application in a damaged stone arch bridge strengthened by using UHPC. Based on the limit analysis method, the collapse mechanisms and load collapse multipliers of Qixingguan Bridge (20 m span heavy load traffic solid belly stone arch bridge) strengthened with UHPC were analyzed, considering good interface bonding and interface debonding between the UHPC layer and the stone substrate. Four UHPC strengthening configurations, including intrados, extrados, wrapping for three sides and for four sides configurations were discussed. The analyses performed indicate that from the perspective of safety, the scheme of adding 12 cm thick UHPC at the intrados of the original arch ring and 10 thick UHPC layer on both sides can be adopted. The construction method of applying UHPC strengthening arch bridge can be referred to the traditional method of increasing the cross-section. The operation condition of the strengthened stone arch bridge is good, which reveals a promising prospect in strengthening existing stone arch bridges with UHPC.