Super-resolution microscopy has revolutionized the fields of chemistry and biology by resolving features at the molecular level. In atomic physics, such a scheme can be furthered to reveal the atomic wavefunction. Here we demonstrate super-resolution imaging based on nonlinear optical response of atoms. With this technique the atomic density distribution can be imaged with a full-width-at-half-maximum resolution of 32(4) nm and a localization precision below 500 pm. The imaging process lasts for only 1 micro-second, which enables us to resolve dynamics of atoms within a single lattice site. A byproduct of our scheme is the emergence of moiré patterns on the atomic cloud, which can immensely magnify atomic density profile by a factor of 100 to 10,000 in the lattice.