Atomic　force　microscopy　(AFM)　is　a　kind　of　high-precision　instrument　to　measure　the　surface　morphology　of　various　conductive　or　nonconductive　samples.　However,　obtaining　a　high-resolution　image　with　standard　AFM　scanning　requires　more　time.　Using　block　compressive　sensing　(BCS)　is　an　effective　approach　to　achieve　rapid　AFM　imaging.　But,　the　routine　BCS-AFM　imaging　is　difficult　to　balance　the　image　quality　of　each　local　area.　It　is　easy　to　lead　to　excessive　sampling　in　some　flat　areas,　resulting　in　time-consuming.　At　the　same　time,　there　is　a　lack　of　sampling　in　some　areas　with　significant　details,　resulting　in　poor　imaging　quality.　Thus,　an　innovative　adaptive　BCS-AFM　imaging　method　is　proposed.　The　overlapped　block　is　used　to　eliminate　blocking　artifacts.　Characteristic　parameters　(GTV,　Lu,　and　SD)　are　used　to　predict　the　local　morphological　characteristics　of　the　samples.　Back　propagation　neural　network　is　employed　to　acquire　the　appropriate　sampling　rate　of　each　sub-block.　Sampling　points　are　obtained　by　pre-scanning　and　adaptive　supplementary　scanning.　Afterward,　all　sub-block　images　are　reconstructed　using　the　TVAL3　algorithm.　Each　sample　is　capable　of　achieving　uniform,　excellent　image　quality.　Image　visual　effects　and　evaluation　indicators　(PSNR　and　SSIM)　are　employed　for　the　purpose　of　evaluating　and　analyzing　the　imaging　effects　of　samples.　Compared　with　two　nonadaptive　and　two　other　adaptive　imaging　schemes,　our　proposed　scheme　has　the　characteristics　of　a　high　degree　of　automation,　uniformly　high-quality　imaging,　and　rapid　imaging　speed.　Highlights:　The　proposed　adaptive　BCS　method　can　address　the　issues　of　uneven　image　quality　and　slow　imaging　speed　in　AFM.　The　appropriate　sampling　rate　of　each　sub-block　of　the　sample　can　be　obtained　by　BP　neural　network.　The　introduction　of　GTV,　Lu,　and　SD　can　effectively　reveal　the　morphological　features　of　AFM　images.　Seven　samples　with　different　morphology　are　used　to　test　the　performance　of　the　proposed　adaptive　algorithm.　Practical　experiments　are　carried　out　with　two　samples　to　verify　the　feasibility　of　the　proposed　adaptive　algorithm.　©　2024　Wiley　Periodicals　LLC.