The　image　super-resolution　via　sparse　representation　considers　that　the　patches　of　images　can　be　represented　by　an　appropriate　over-complete　dictionary,　so　sparse　coefficients　of　low-dimensional　space　are　mapped　into　high-dimension　one　for　synthesizing　high-definition　patches.　We　propose　a　face　super-resolution　based　on　sparse　representation　with　position　weights　method,　which　use　the　positional　relationship　between　target　patch　and　the　sample　atom　as　the　criteria　for　atomic　matching,　to　improve　the　accuracy　of　atomic　basis　selection　and　reduce　the　computational　complexity.　Experimental　results　demonstrate　the　proposed　face　super-resolution　based　on　sparse　representation　with　position　weights　method　outperforms　the　traditional　schemes　significantly　both　in　subjective　and　objective　quality.