The invention provides a washing machine heat dissipation wheel fastening tool and a fastening method thereof. The fastening tool comprises a base, a first force transfer component which is arranged on the base and can be matched with a screw cap of a bolt, and a second force transfer component which is arranged on the base and can be matched with a nut, the first force transfer component and the second force transfer component transmit rotating torque on the base to the bolt and the nut and drive rotating installation of the bolt and the nut, and a first set torque transmission component is arranged between the first force transfer component and the base; when the bolt is fastened in place, the rotating torque on the base continues to be transferred to the second force transfer component and drives the nut to rotate and be fastened. In this way, in one working procedure, the first force transfer component does not continue to transfer torque after driving the bolt to be installed in place, the second force transfer component continues to transfer the torque to the nut, the bolt and the nut can be fastened through one working procedure, the bolt can be fixed firmly, and the installation efficiency is improved.