Super-resolution　image　reconstruction　has　recently　drawn　considerable　attention　within　the　research　area.　For　some　special-purpose　imaging　devices　such　as　medical　imaging,　remote　sensor　imaging　and　video　capturing,　the　acquired　images　cannot　often　achieve　a　higher　resolution　because　of　the　limitation　of　imaging　mechanism　and　imaging　sensor.　Super-resolution　image　reconstruction　methods　attempt　to　create　a　single　high-resolution　and　high-quality　image　from　multiple　low-resolution　observations　(or　a　video　sequence)　degraded　by　warping,　blurring,　noise　and　aliasing.　So　far,　existing　super-resolution　methods　are　all　confronted　with　the　problem　of　slow　convergence　and　expensive　computation.　To　satisfy　the　requirement　of　real-occasion　applications,　a　fast　super-resolution　reconstruction　algorithm　is　built　upon　the　MAP　framework.　In　the　proposed　algorithm,　two　improvements　are　presented　to　reduce　the　high　computational　complexity　of　the　standard　MAP　algorithm.　The　first　improvement　is　to　compute　directly　the　increment　of　the　MAP　objective　function　as　the　component　of　the　gradient　vector,　which　avoids　the　redundant　computation　of　the　objective　function.　The　second　one　is　to　select　the　Armijo　rule　to　identify　the　step　size,　which　avoids　the　computation　of　the　computationally　demanding　Hessian　matrix.　Experimental　results　show　that　the　computation　time　is　reduced　significantly,　whereas　the　solution＇s　convergence　is　guaranteed　and　the　similar　quality　is　maintained.