This invention relates to a mounting structure (1) for mounting a turboprop (2) under an aircraft wing (4), the structure comprising a rigid structure (8) provided with an aft underwing box (10), and at least one forward rigid segment (12, 14), each forward rigid segment having two transverse frames (30, 32, 54) at a spacing from each other. According to the invention, at least one forward rigid segment (12, 14) of the rigid structure also comprises at least one forward upper box (34, 56) connecting a top part (30a, 32a, 54a) of the two transverse frames (30, 32, 54) of the forward rigid segment.