The invention relates to a rigid inside and outside tooth-profile-wrapped tooth reducer which comprises a first level reducing mechanism and a second level reducing mechanism. The first level reducing mechanism comprises an eccentric wheel (101), a first turning arm bearing (5), an outer meshing curve wheel (7) and a gear pin (8), wherein the gear pin (8) is fixed on a first support (9) and is meshed with the outer meshing curve wheel (7) in an external mode. The second level reducing mechanism comprises an eccentric driving wheel (14), a second turning arm bearing (13), an inner meshing curve wheel (11) and an output disc (16), wherein the inner meshing curve wheel (11) is meshed and matched with the gear pin (8) in an internal mode, the output disc (16) is connected with an output shaft (20) of the output disc (16) in a linkage mode, the eccentric driving wheel (14) is connected with the outer meshing curve wheel (7) in a transmission mode through a pin (26), the inner meshing curve wheel (11) is connected with the output disc (16) in a transmission mode through a transmission pin (24), one side of the outer meshing curve wheel (7) is provided with a first reinforcing bracket (6), and one side of the inner meshing curve wheel (11) is further provided with a second reinforcing bracket (23). The rigid inside and outside tooth-profile-wrapped tooth reducer has the advantages of being small in the number of teeth, large in speed ratio, small in size, high in bearing and efficiency, long in service life, high in rigidity, and particularly suitable for a reducer for a heavy-load robot.