In view of the problems of matching pursuit algorithms in signal sparse decomposition, we propose a method to detect harmonics and inter-harmonics based on atomic decomposition, which is optimized by the imperialist competitive algorithm ( ICA) and orthogonal matching pursuit algorithm (OMP). First, the Gabor dictionary is simplified to the sinusoidal dictionary according to the characteristics of harmonics and inter-harmonics. Then, the signals are decomposed by using the OMP algorithm. In which, the number of iterations is determined by the reasonable threshold of correlation and energy. Finally, the estimation of parameters is obtained based on the index parameters of the most matching atoms. The introduction of ICA in the iterative process of OMP can search for the best matching atoms in the continuous parameter space, which avoids the limitation of index parameter step size on detection accuracy. Simulation results show that the proposed algorithm can detect each harmonic and inter-harmonic component with high accuracy, even under noisy conditions. The error of frequency, amplitude, and phase are less than 0. 015 4% , 0. 722 4% , and 1. 512 6°, respectively. In addition, the proposed algorithm has the ability to detect inter-harmonics with closing frequencies and locate the time-varying harmonics and inter-harmonics. Compared with the orthogonal matching pursuit algorithm, the computational complexity is reduced by more than 99% .