We propose a type of diffractive optical element, a modified Fibonacci photon sieve (MFiPS), designed by using the Fibonacci sequence with two different initial seed elements. Focusing properties of MFiPS show that it not only has less secondary foci, but also presents two equal intensity foci by optimizing the diameters of pinholes of MFiPS whose ratio of the two focal distances approaches the golden mean. Higher transverse resolution on the two focal spots is improved by using a super-Gaussian amplitude modulation technology.