The invention provides a reinforced concrete combined arch bridge spanning karst caves in a tunnel and a construction method thereof. The arch bridge comprises a plurality of profile steel arch ribs arranged in parallel. The two ends of each section steel arch rib are fixedly connected with arch supports poured on the two side walls of the karst cave; a certain distance is reserved between every two adjacent profile steel arch ribs, the adjacent profile steel arch ribs are connected through a plurality of cross beams, supporting steel plates are laid on the cross beams, a concrete arch rib ispoured on the tops of the steel plate supports and the profile steel arch ribs, a concrete filling layer is poured on the top of the concrete arch rib, and the top face of the concrete filling layer is flush with the tunnel bottom face. During construction, firstly, profile steel arch rib installation is completed through vertical rotation construction; then the profile steel arch ribs are used asthe support to construct the upper concrete arch ribs, the characteristics that the profile steel arch rib is small in dead weight, high in strength and convenient and fast to install are fully utilized, formwork supports are prevented from being erected under a bridge, and therefore construction difficulty is lowered, construction quality is guaranteed, safety risks are reduced, and constructioncost is reduced.