The invention relates to the field of metal machining, in particular to a workpiece installing and positioning fixture of an internal thread grinding machine. The fixture is composed of a machine tool connecting element (1), a main body element (2), a radial positioning element (14), a fast clamping device, an axial positioning device and a reset device. Compared with the prior art, the outer circle of a workpiece and a rack serve as the positioning basis, positioning is reliable, requirements for workpiece spiral roller path, outer circle and rack position precision are met, and switching of workpieces of different types can be quickly achieved after positioning parts of the fixture are replaced. When the fixture is used for machining an automobile steering gear nut and thread arc roller path on the numerically-controlled internal thread grinding machine, the grinding machine needs to be adjusted just when a first workpiece is to be machined, then the workpieces can be efficiently machined in a high-precision mode, time spent in installing and fixing the workpieces is greatly saved, and time spent in adjusting the grinding machine for each workpiece is saved as well.