In　order　to　reduce　greatly　computational　cost　and　storage　requirement,　three　two-dimensional　(2D)　gradient　algorithms　for　fast　super-resolution　image　reconstruction　was　presented　by　minimizing　the　smooth　cost　function.　To　enhance　estimation　accuracy　of　super　resolution　image　reconstruction,　this　paper　proposes　a　2D　subgradient　algorithm　for　super-resolution　image　reconstruction.　Compared　with　the　existing　2D　gradient　algorithms,　the　proposed　2D　subgradient　algorithm　can　minimize　a　novel　nonsmooth　cost　function　with　an　l1-norm　learning　term　and　TV　term.　Simulation　results　show　that　the　proposed　2D　subgradient　algorithm　has　better　performance　in　terms　of　both　PSNR　and　visual　quality　than　the　existing　2D　gradient　algorithms.　©　2016　IEEE.