Abstract: The iterative nonuniform fast Fourier transform (NUFFT) algorithm for the low side lobe level pattern synthesis of unequally spaced arrays is presented. Through the strict mathematical derivation, a correspondence relationship between nonuniform discrete Fourier transform(NUDFT) and array factor is established. With the linear combination of over sampling FFT coefficient express complex exponential function approximately, finally it effectively reduces the peak side lobe level of linear array by interpolation and iteration. The effectiveness and efficiency of iterative NUFFT will be demonstrated for equally spaced and unequally spaced arrays, which are compared with PSO algorithm.