A single-layer reflecting element is proposed based on the principle of linear-to-circular polarization conversion focusing metasurface, which can independently control the phases of x-polarized and y-polarized reflecting waves and operate in a broadband of 10-14 GHz. Following the generalized Snell's laws of reflection, a super cell is designed with a phase-gradient of -60 for x-polarized waves and 60 for y-polarized waves, and the simulation results show the well wideband anomalous reflection as expected. In the design of the multifunctional metasurface, the 1313 unit cells are used to satisfy the parabolic profile and the focal-distance-to-diameter ratio is set to be 0.5. The phase compensation for forming a constant aperture phase is provided by the individual reflected elements with different structure parameters and x-y=90 is used to realize polarization conversion. The designed sample is simulated in CST Microwave Studio and the results show that both of the x-polarized and y-polarized plane waves are well focused through the reflection of the focusing metasurface in a broadband of 10-14 GHz. Traditionally, multi-layer element is used to broaden phase coverage and bandwidth, the single-layer design in this paper greatly reduces the cost, processing difficulty and thickness of the lens. For further application, a linearly polarized Vivaldi antenna with a highest gain of 10 dB is located at the focal point of metasurface and the angle included between its polarization direction and x-axis is 45 in order to acquire right-handed circularly polarized reflecting wave. According to the reversibility principle of electromagnetic wave propagation, the spherical wave radiated by the feed antenna is converted into plane wave by the reflection of the focusing metasurface so that the antenna gain is remarkably enhanced. Simultaneously, the linearly polarized wave can be transformed into circularly polarized wave. Finally, the feed antenna and the metasurface are fabricated, assembled and measured. Numerical and experimental results are in good agreement with each other, which shows that the -1 dB gain bandwidth of the high-gain antenna is 24% (11-14 GHz) and the 3 dB axial ratio bandwidth is 29.8% (10-13.5 GHz). In addition, the gain at 12 GHz reaches a highest value of 19.6 dBic, and the aperture efficiency is more than 54%. The good performances indicate that the proposed broadband high-gain circularly polarized antenna has a well promising application in various communication systems. It is worth noting that the horizontally polarized, vertically polarized, right-handed circularly polarized and left-handed circularly polarized high-gain antenna can be realized with the rotation of feed antenna. In this case the idea is more versatile and valuable for designing the polarization reconfigurable antenna systems.