An ultrathin flat metalens that experimentally realizes three-dimensional microwave manipulation has been demonstrated as able to approach the theoretical limit of cross-polarization (cross-pol) conversion efficiency of the transmission, as predicted by Monticone et al (2013 Phys. Rev. Lett. 110 203903). The helicity-dependent phase change is introduced to the transmission and can be engineered by assembling the spatial orientation of each Pancharatnam–Berry phase element. By realizing the constant phase gradients in orthogonal directions, an anomalous non-coplanar refraction is unanimously demonstrated in the three-dimensional space under the circular-polarized incidence, and the refraction angle is well predicted with the generalized Snell's law, derived with phase gradients in orthogonal directions. More importantly, the maximum conversion efficiency of the cross-pol transmission is as high as 24%, which approaches the upper-bound of the theoretical limit. The proposed metalens has only a single layer as thin as 0.001 λ, which massively reduces the thickness of the microwave lens along the wave propagation direction. With the great improvements in efficiency and the thickness reduction, as well as the excellent non-coplanar refraction, our design provides a promising approach to miniaturize, planarize and integrate multiple microwave components.