Detecting the harmonic currents fast and precisely in non-linear loads are very important to suppress harmonics. Among different detection methods, the detection method based on instantaneous reactive power theory is considered as one of the simplest and most attractive techniques. However, the speed and accuracy of the detection method for single-phase system are seriously affected by the fluctuation of the output of low-pass filters (LPFs) and the correctness of fictitious orthogonal components. To address these issues, the inherent relations between the output of LPFs and the harmonic currents of the loads are discussed. A recursive module is proposed to suppress the fluctuation of the output of LPFs, which is mainly caused by the two dominant harmonic currents in non-linear loads. Based on recursive modules, a recursive harmonic current detection method, which is little affected by the two dominant harmonic currents, is presented in the paper. In addition, to eliminate the effects of inaccurate orthogonal current in traditional detection methods, coordinate transformation modules without the use of fictitious orthogonal components are adopted. Simulation and experimental results show that the proposed current detection method has high detection accuracy in steady-state scenarios and fast dynamic responses under load change, voltage sag and frequency variation can be achieved with the proposed detection method.