Metasurfaces have been widely studied for the arbitrary manipulation of the amplitude, phase and polarization of a field at the subwavelength scale. Holographic images with a high resolution and a large viewing angle can be reconstructed from phase-only holograms encoded in a metasurface. The quality of a holographic image can be greatly improved by using complex-amplitude holograms. However, realizing a high efficiency metasurface with simultaneous and independent control of the amplitude and phase remains a great challenge. In this work, an ultrathin dielectric metasurface which can modulate the complex amplitude in the transmission mode is proposed for a metasurface hologram. The amplitude is controlled by adjusting the dipoles and quadrupoles by tuning the geometric size. The phase value from 0 to 2π is manipulated based on the Pancharatnam–Berry phase (also called the geometric phase) by rotating the meta-atom. The experimental results show that a three-dimensional image reconstructed from a complex-amplitude hologram presents better quality than that from a phase-only hologram. The proposed metasurface shows great potential for applications that require complex amplitude modulation.