The invention discloses a device for machining a concave arc surface of a part by using a common horizontal lathe. The device comprises a fixed plate installed on a tailstock base. A lengthening plateis fixedly installed on a transverse end face of a middle supporting plate. A first hinge pin is installed on the upper surface of the inner end of the fixed plate. A second hinge pin is installed onthe upper surface of the lengthening plate. The first hinge pin and the second hinge pin are together sleeved with a chain connecting plate through copper sleeves respectively. The invention furtherdiscloses a method for machining the concave arc surface of the part by using the common horizontal lathe. The method comprises the steps of firstly, installing a machining conversion assembly on thecommon horizontal lathe; secondly, positioning a workpiece as a machining object; thirdly, carrying out tool setting; fourthly, machining the concave arc surface, wherein a sliding box is controlled to drive a large supporting plate to lengthways move along a lathe body, the chain connecting plate is enabled to rotate with the first hinge pin as the center, the second hinge pin is used for carrying out transmission to enable a turning tool to carry out circular motion with the radius R so that the concave arc surface with the radius R can be machined on the workpiece, and the operation is repeated till the concave arc surface of the workpiece meet the machining requirements of a drawing.