We provide a position-patch based face hallucination method using convex optimization. Recently, a novel position-patch based face hallucination method has been proposed to save computational time and achieve high-quality hallucinated results. This method has employed least square estimation to obtain the optimal weights for face hallucination. However, the least square estimation approach can provide biased solutions when the number of the training position-patches is much larger than the dimension of the patch. To overcome this problem, this letter proposes a new position-patch based face hallucination method which is based on convex optimization. Experimental results demonstrate that our method is very effective in producing high-quality hallucinated face images.