The demands for highly directive antennas are becoming more stringent, especially in microwave regions. Traditional ways to enhance the antenna gain such as reflectors, dielectric lenses, waveguide horns and microstrip antenna arrays suffer design complexity, high cost and power loss in the feeding network, so it is urgent to find a simple way to solve the problem. Fabry-Perot (F-P) antenna has a high directivity and low sidewall, owing to the resonance of the cavity in a cophasal and tapered field distribution along the lateral direction. However, the disadvantage of F-P antenna is obvious for the inherently narrow gain bandwidth which inhibits their many applications. In this paper, a broadband and high-gain shared-aperture F-P resonator magneto-electric (ME) microstrip antenna working at X band is designed and fabricated. In order to design a wideband metamaterial superstrate unit, the structure with two different frequency selective surface (FSS) layers is presented: the metal pattern at the top of the unit is a square patch and has a high reflection coefficient in the high frequency band, and at the bottom the metal pattern is a cross patch, it has a high reflection coefficient in the low frequency band, therefore, the whole unit should resonate in a broadband frequency range. Theoretical analysis and simulation result indicate that the unit has a linearly increasing phase response and a high reflection coefficient across a broadband range and it has the potential to construct a wideband F-P resonator antenna. In the proposed antenna, a novel wideband ME microstrip antenna is used as the feeding source. For the antenna covers the whole X band, the bandwidth of the F-P resonator superstrate should be further expanded. Simulated calculation results indicate that different sizes of two-layer FSSs have different reflection phases but the same coefficient, therefore a shared-aperture structure with three different sizes of FSSs is obtained. The arrangement utilizes the phase compensation property along different FSSs, and broadens the gain enhancement bandwidth effectively. When the superstrate is set to be approximately 15.5 mm above the ground plane of the ME antenna, the antenna possesses an impedance bandwidth of 44.7% for the reflection coefficient (S11) below -10 dB from 7.8 GHz to 12.3 GHz, covering the whole X band. From 7.9 GHz to 12.1 GHz, the antenna has an obvious gain enhancement, with a peak of 7 dB. Numerical and experimental results indicate that compared with the traditional F-P resonator structure, the shared-aperture metamaterial superstrate can effectively broaden the antenna gain enhancement bandwidth, and it has great application values for designing new broadband metamaterial superstrate high-gain antennas.