Atomic force microscopy (AFM) is a very useful measurement instrument. It can scan the conductive and nonconductive samples and without any restriction in the environments of application. Therefore, it has become an indispensable micro-/nano-scale measurement tool. However, controller of the conventional AFMs do not consider the dynamic characteristics of the scan trajectory and mostly use raster scanning easily to induce the mechanical resonance of the scanner. In an attempt to improve these problems for increasing the scan speed and accuracy, we designed an internal model principle (IMP) based neural network complementary sliding mode control (NNCSMC) for tracking a smooth Lissajous trajectory, which can allow an effectively increasing in the scan speed without obviously sacrificing in the scan accuracy. To validate the effectiveness of the proposed scan methodology, we have conducted extensive experiments and promising results have been acquired.