In order to improve the computational speed and prior background noise-dependent problem of single molecule localization algorithm, a Fourier domain localization scheme based on zero-padded fast Fourier transform and phase gradient operators is used to obtain a powerful mathematical model for localizing a single molecule without numerical fitting. Numerical simulations indicate that the proposed method exhibits nanometer scale localization precision while executing almost as fast as the fluoroBancroft algorithm. Furthermore, a sample consisted of several lines of molecules are simulated imaged. The results demonstrate that two lines of molecules separated by 30 nm can be resolved. Finally, super-resolution images of filopodia in HeLa cells are reconstructed based on the method, in which filopodia with diameter of 75~200 nm are resolved.