Background subtraction is a major part of many motion detection, tracking and surveillance systems. In this paper a new algorithm for the purpose of the background model initialization has been presented. The key idea of the proposed method lies in the identification of the background based on QRDecomposition method in linear algebra. R-values produced with QR-Decomposition can be applied to decompose a given system to indicate the degree of the significance of the decomposed parts. We split the image into small blocks and select the background blocks with the weakest contribution, according to the assigned R-values. The main advantage of the proposed method is that in contrast to many other methods, here, there is no need for an empty scene with no foreground object. Simulation results showed that the proposed method produced better background model with respect to some others.