Photon sieve is a novel nanostructure element with an array of pinholes. After structural optimization of pinholes, it has good focusing ability from short, visible or long-wavelength light. The resolution of the photon sieve depends on the diameter of the outermost pinholes. To improve the resolution, the diameter of the outmost pinholes decreases. At present, the design theory commonly adopted is scalar diffractive theory. But it is well known that scalar diffractive theory is no longer valid for designing of photon sieves when the diameter of pinholes is less than the wavelength of the incidence light. In this paper, an amplitude photon sieve is designed using vector diffractive theory. The detailed design procedures are described. To compare the imaging performance, we analyze the Fresnel zone plates and photon sieves using numerical simulation. The results show that photon sieves have better focusing performance than Fresnel zone plates, but the diffractive efficiency is lower than Fresnel zone plates. The results also provide a theoretical foundation for the application of photon sieves. To improve the diffractive efficiency, future work will focus on structural amelioration of photon sieves, e.g., phase photon sieves. We also provide two potential structures of phase photon sieves.