In the design of scroll wrap profiles, aiming at the problem of lacking of simple and effective general geometric model and the preference of scroll profile geometric performance is not taken into consideration in practical engineering applications, a new method of constructing scroll wrap profiles applying the frenet moving frame was proposed. Firstly, a frenet moving frame was attached to the curve of scroll wrap profile to replace the fixed Cartesian Coordinate System. Then, using the curvature of the plane curve and frenet moving frame to express the intrinsic characteristics of the scroll wrap profiles, a general geometric model of scroll wrap profiles with curvature and frenet moving frame as parameters was established. Finally, the mapping relationship between the control coefficients and the geometric performance of the scroll wrap profiles was set up. On this basis, taking the engineering application of scroll compressor as the design goal, under the condition that the circumferential diameter of scroll plate as well as the tooth thickness were known respectively, by using the mapping relationship, a series of control coefficients were selected according to the preferences of the design requirements, then the scroll wrap profiles that satisfy the requirements were constructed. The results show that the scroll wrap profile constructed by frenet moving frame not only includes all types of scroll wrap profiles at present, but also reconstructs them according to the expected geometric performance, so as to design the scroll wrap profiles with the best performances. This method lays a theoretical foundation for the flexible design of scroll compressor profile.