The thermal deformation error of CNC machine tools is the main factor affecting the working accuracy.In view of the problem that current thermal error of machine is difficult to solve, a thermal error modeling and compensation principle was proposed combined with the fuzzy clustering theory, grey relation theory and multivariate linear regression theory. By the selfdeveloped AGPM in laboratory, the accurate thermal error compensation model was established through the optimal analysis of the temperature field measure points and the multiple linear regression compensation model solving. Through compensation verification, the principle is correct, simple, stable and reliable. The thermal deformation error of machine tool can be significantly reduced by using it.