Two Dimensional Locality Preserving Projection (2DLPP) is a recent extension of LPP, a popular face recognition algorithm. It has been shown that 2D-LPP performs better than PCA, 2D-PCA and LPP. However, the computational cost of 2D-LPP is high. This paper proposes a novel algorithm called Ridge Regression for Two Dimensional Locality Preserving Projection (RR2DLPP), which is an extension of 2D-LPP with the use of ridge regression. RR-2DLPP is comparable to 2DLPP in performance whilst having a lower computational cost. The experimental results on three benchmark face data sets − the ORL, Yale and FERET databases − demonstrate the effectiveness and efficiency of RR2DLPP compared with other face recognition algorithms such as PCA, LPP, SR, 2D-PCA and 2D-LPP.