As a novel diffractive optical element, photon sieve has good focusing properties. We propose a method to verify the focusing properties by using apodized photon sieves. The apodized photon sieve is obtained by using a Gaussian window function to modulate the general photon sieve. Focusing properties of apodized photon sieve are studied by numerical simulations and experiments. It shows that photon sieves have good focusing ability, and the focusing ability of the photon sieve on the focal plane is stronger than that on other image planes. The experimental results also demonstrate that photon sieves can be used to generate optical vortices. The existence of optical vortices is confirmed by the formation of fork fringes. This apodized photon sieve is expected to have some practical applications in focusing analysis, optical imaging, and optical communication.