The invention provides a construction method of a reinforced concrete arch bridge and belongs to the technical field of bridge construction. The construction method comprises the following steps of (1) assembling of an arch frame, (2) prepressing of an arch ring and the arch frame, (3) laying of arch ring formworks, (4) binding of steel bars, (5) concrete segmented pouring construction and (6) unloading and removing of the arch frame. According to the construction method of the reinforced concrete arch bridge, aiming at the problem that as for bridges in deeply mountains, full space supports cannot be erected for arch ring concrete cast-in-situ construction due to the terrain limitation, the construction technology that the non-supporting-pier 64-type military beam assembling arch frame iscombined with sand cylinders for unloading and frame removing is adopted, and the construction method has the advantages of less investment, short construction period, high operability, high standardized degree and the like; and based on the principle that the engineering requirements can be met and the economical and applicable principles, the adopted construction method is simple and flexible,and significant economic and social benefits can be achieved.