The increasing use of non-linear loads may cause harmonics and interharmonics components in power system signals. The methods used for estimating these components must consider different requirements for practical applications, such as low error rate, robustness to noise and fundamental frequency deviation, needlessness of previous knowledge of the model order, and short execution time. This work proposes a new algorithm called Anti-Leakage Matching Pursuit (ALMP) that can estimate harmonics and interharmonics mainly under noise and frequency deviations. The algorithm is based on the Matching Pursuit method, and its principal stage consists of solving a non-linear least squares problem. The proposed method was compared to other recent techniques, such as Matrix Pencil Method (MPM), Fast Matching Pursuit (FMP) and Harmonics and Interharmonics components Estimation based on Signal Sparse Decomposition (HIESSD), besides the most used algorithm – the Discrete Fourier Transform (DFT). The proposed algorithm obtained results equivalent to the existing algorithms for harmonics and interharmonics estimation, without requiring prior model order selection. It also proved to be more robust to frequency deviation and presented a reduced execution time than the other algorithms.