A broadband high-gain low-profile antenna based on gradient size metasurface is proposed. The antenna is composed of a double-layer metasurface and a layer of microstrip slot. The double-layer metasurface is composed of gradient size hexagonal array patches printed on two dielectric plates respectively. There are non-equidistant gaps between these patches. This gradient design of the metasurface unit size can generate multiple adjacent resonance points to broaden the bandwidth. The antenna's bandwidth radiation characteristics are analyzed by changing the size and structure of the metasurface antenna. In order to obtain the best broadband performance, genetic algorithms are employed to optimize the antenna geometric parameters. To verify the simulation results, a sample antenna with a side length of 43.3 mm and a thickness of 4.853 mm is fabricated and tested. The actual measurement results show that the -10 dB impedance bandwidth of the antenna reaches 54% (3.99~6.93 GHz), the highest gain reaches 12.05 dB, and the gain remains above 8 dB in 4~6 GHz range. Therefore, the antenna realizes the characteristics of wide frequency band, high gain and low profile, and can be applied to many fields of wireless communication.