Single　image　super-resolution　(SISR)　is　the　process　of　reconstructing　a　high-resolution　(HR)　image　to　compensate　for　the　lost　high-frequency　information　from　only　a　single　low-resolution　(LR)　image.　Blind　image　super-resolution　attempts　to　reconstruct　the　HR　image　when　the　blur　kernel　is　unknown,　which　is　an　ill-posed　inverse　problem.　We　propose　an　alternating　optimization　based　self-supervised　blind　image　super-resolution　method　(Self-SR),　which　models　a　joint　optimization　problem　about　the　blur　kernel　and　the　HR　image　and　estimates　them　by　iteratively　alternating　the　deep　network　and　the　regularization　model.　The　deep　convolutional　neural　network　learns　complicated　features　to　represent　the　HR　image　without　requiring　smoothness　regularization　since　data　fitting　is　inherently　free　from　noise　amplification.　The　simple　blur　kernel　is　modeled　using　the　regularized　least-squares　model,　which　admits　the　direct　closed-form　solution　for　the　blur　kernel.　Self-SR　incorporates　the　learning　ability　of　the　deep　network　and　the　generalizability　of　the　optimization-based　model,　and　with　the　help　of　the　blur　kernel　estimated　by　the　regularization　model,　the　data　fidelity　loss　function　with　the　supervision　of　the　LR　image　facilitates　the　deep　network　to　solve　image　super-resolution　tasks　with　the　more　accurate　blur　kernel.　Experimental　results　on　synthetic　and　real　LR　images　show　that　Self-SR　achieves　better　super-resolution　performance　than　most　blind　and　non-blind　methods.