Abstract: Sparse Frequency Waveform (SFW) can be transmitted by radar systems to overcome narrowband interferences. However, SFW suffers the raised range sidelobes generally, leading to worsening detection performance for weak targets. To solve this problem, a method to design a phase-coded SFW with low range sidelobes is proposed in this paper. The objective function is constructed according to jointly minimizing the mean square error of the power spectrum density with range sidelobes. The Cycle Iterative Algorithm (CIA) based on Fast Fourier Transform (FFT) is put forward to search for the optimal phase-coded waveform. The proposed method is then extended for Multiple-Input Multiple-Output (MIMO) radar to design a set of phase codes of SFW with good auto-/cross-correlation performances. The presented method searches along the direction making sure the objective function nonincreasing and need not compute conjugate gradient. It has a low computation complexity and can be used to design and update the transmit waveform rapidly. Simulation results demonstrate the effectiveness and flexibility of the proposed method.