Recently sparse and collaborative representation based classification has been developed for face recognition with single sample per person (SSPP). By using variations extracted from a generic training set as an additional common dictionary, promising performance has been reported in face recognition with SSPP. However, existing representation based classifiers for face recognition with SSPP ignored to make full use of the discrimination of particular facial regions (e.g., eyes and nose), which have a high detection rate in various facial variations. Since the particular regions only cover a certain part of the face, the regular regions (e.g., dense sampling points) are also utilized to represent the face completely. In this paper we proposed a robust local representation (RLR) model for face recognition with SSPP by fully exploiting the features of both particular and regular facial regions. Thus variation-robust features of particular facial regions and dense features of regular facial regions are both captured, while bad features with big variations are adaptively given low weight values by the proposed RLR so that they contribute little to the representation and classification. Experimental results on AR and LFW databases demonstrate that the proposed RLR method has achieved better results than the state of the art methods.