A new photon sieve with Fibonacci sequence is proposed and a focusing and imaging model of the Fibonacci photon sieve (FiPS) is presented based on the Huygens-Fresnel principle.The results show that the FiPS presents two longitudinal foci with the ratio of golden mean.When the diameters of pinholes are equal to 1.165 times the width of corresponding orbits,the intensity of the two foci is almost the same.Compared with the resolution of Fibonacci zone plate (FiZP),FiPS has higher transverse resolution.Finally,higher transverse resolution on the two focal planes is improved by applying Gaussian apodized technology to the numbers of pinholes of FiPS.In consequence of smaller size,lighter weight,more flexible design and bifocal property,the FiPS can be applied to optical switches,nanometer lithography,bionic eyes,multi-focus imaging and ranging,even some new applications such as ranging from X-ray microscopy and THz imaging.