In this paper, we present a novel iterative MPEG super-resolution method based on an embedded constraint version of Adaptive projected subgradient method [Yamada & Ogura 2003]. We propose an efficient operator that approximates convex projection onto a set characterizing framewise quantization, whereas a conventional method can only handle a convex projection defined for each DCT coefficient of a frame. By using the operator, the proposed method generates a sequence that efficiently approaches to a solution of super-resolution problem defined in terms of quantization error of MPEG compression.