In linear optics, the metasurface represents an ideal platform for encoding optical information because of its unprecedented abilities of manipulating the intensity, polarization, and phase of light wave with subwavelength meta-atoms. However, controlling various degrees of freedom of light in nonlinear optics remains elusive. Here, we propose a nonlinear plasmonic metasurface working in the near-infrared regime that can simultaneously encode optical images in the real and Fourier spaces. This is achieved by designing a diatomic meta-molecule, which enables the independent control of the nonlinear geometric phase, polarization, and intensity of second harmonic waves. The proposed nonlinear diatomic metasurface provides an ultracompact platform for implementing multidimensional optical information encoding and may hold great potential in optical information security and optical anticounterfeiting.