Reconstructing a colour constant reflectance function under various practical light sources is important in some of practical applications. Linear programming method was proposed by Takahama and Nayatani (1973), and Berns et al (1985) respectively. Their methods were derived based on minimisation in the tristimulus values colour space in order to avoid nonlinear optimisation. In this paper a least-square method was derived for reconstructing reflectance functions based upon the concept of colour constancy. The main contributions of this method are a) directly using colour difference as a measure of colour constancy; b) avoiding highly nonlinear optimisation; c) generating much smooth reflectance with very good colour inconstancy index.