With the field of science research is more and more widespread, to solve large-scale over determined system of linear equations has become a key problem, and the use of parallel processing technology also become the trend of the research. Firstly, in this paper we introduce the basic principle of the Serial least squares algorithm of the curve fitting, and based on the least square principle, we found an parallel least squares curve and surface fitting method; Secondly, combined with QR decomposition, we further improve the parallel least squares fitting algorithm. We also solve the problem of over determined system of linear equations and the curved surface fitting question in threedimensional space. Finally, through the specific examples, comparing the scatter diagram to the fitting chart and considering the serial and parallel computing time, we can show the advantages and effectiveness of this method.