The invention discloses a multi-axis linkage speed reducer which comprises a speed reducer, a coupling, a motor, a first bracket, a pair of support rods, a first hydraulic cylinder, a first piston rod, a first guide rail, a second guide rail, a second bracket, a third bracket, a fourth bracket, a second hydraulic cylinder, a second piston rod, and the like. By fixed or articulated connection among all parts, the speed reducer obtains power rotating around a Z axis when starting the first hydraulic cylinder; and the speed reducer obtains power moving along the direction of an X axis when starting the second hydraulic cylinder. The design concept can also realize the movement and rotation of the speed reducer along other coordinate axes by different connection among the parts. The design overcomes the defect of unavailable movement of the traditional speed reducer after foundation distribution is finished, can realize that the same speed reducer is used in different positions, saves the investment cost, simplifies mechanism facilities and is suitable for the connection drive of machine tools of special industries, such as metallurgy, mine, wood, excavation, and the like.