Amplitude and phase controllable metasurfaces are proposed to suppress the sidelobe levels (SLLs) of a metasurface lens (metalens). The amplitude-control metasurface is responsible for controlling the transmission amplitude with its unit cells’ phase shift variation less than ±10°. The phase-control metasurface is responsible for transferring the spherical incident waves to plane waves with its unit cell covering 360° transmission phase shift, while the transmittance remains higher than −1 dB. Both the metasurfaces are with symmetrical structures for dual-polarization. By integrating the amplitude and phase controllable metasurfaces, a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$9.7\lambda _{0} \times 9.7\lambda _{0}$ </tex-math></inline-formula> metalens operating at 28 GHz 5G bands is designed and successfully suppresses the SLL. Within the 3 dB gain bandwidth from 26.0 to 29.0 GHz, this metalens antenna achieves the SLL lower than −20.9 dB in H-plane and lower than −17.3 dB in E-plane. The maximum gain is 23.4 dBi at boresight, and the achieved SLL is −16.3 dB as its scanning angle reaches the maximum of ±29°. Compared with the phase-only metalens, the proposed metalens antenna realizes the maximum and minimum SLL suppression of 9.8 and 3.4 dB within the 3 dB gain bandwidth at a price of a gain drop of 0.8 dB at the designed frequency.