Atomic　force　microscopy　(AFM)　is　a　kind　of　high-precision　nanoscale　instrument　to　measure　the　surface　morphology　of　various　samples.　Nevertheless,　the　standard　AFM　scanning　process　takes　a　very　long　time　to　obtain　high-resolution　images.　Compressive　sensing　(CS)　can　be　used　to　achieve　fast　AFM　imaging.　But,　the　traditional　CS-AFM　imaging　is　difficult　to　balance　the　image　quality　of　each　local　area,　resulting　in　poor　quality　in　the　object　area　at　low　sampling　rate.　Therefore,　a　novel　imaging　scheme　of　adaptive　CS-AFM　is　proposed.　The　fast　scanning　is　first　used　to　generate　a　low　resolution　image　in　a　short　time,　and　then　bicubic　interpolation　is　performed　to　obtain　a　high　resolution　image.　Afterwards,　an　advanced　detection　algorithm　is　used　to　realize　the　accurate　detection　and　positioning　of　the　objects.　Furthermore,　the　supplementary　scanning　is　carried　out　to　achieve　adaptive　sampling　on　the　objects.　After　sampling,　the　measurement　matrix　corresponding　to　the　measurement　points　is　constructed.　Finally,　Total　Variation　Minimization　by　Augmented　Lagrangian　and　Alternating　Direction　Algorithm　(TVAL3)　is　used　to　reconstruct　the　whole　AFM　image.　The　imaging　quality　of　the　sample　is　analyzed　and　assessed　by　image　evaluation　metrics　(PSNR　and　SSIM)　and　visual　effect.　Compared　with　two　non-adaptive　imaging　schemes,　the　proposed　scheme　is　characterized　by　high　automation,　short　time,　and　high　quality.　©　2021