When a discrete Fourier transform (DFT) is used to detect a grid signal containing harmonics and interharmonics with similar frequency, the non-synchronous sampling of the signal causes spectrum leakage and aliasing, which seriously affect the detection accuracy. In order to improve this, a harmonic and interharmonic detection algorithm based on DFT and group harmonic energy recovery theory is proposed. First, from a spectrum analysis of the harmonic / interharmonic by DFT, the number of harmonic and interharmonic components is determined. Then based on group energy recovery theory, the length of the sampling window is automatically adjusted by the frequency offset, and the collapse energy around the main harmonic / interharmonic is collected iteratively. Finally, the amplitude and frequency are restored to their original state by total collapse energy value around the main harmonic / interharmonic, and the accurate values of the amplitude and frequency of each component can be obtained. Simulation in Matlab shows that the proposed algorithm can effectively reduce the measurement error caused by spectrum leaks, and accurately measure the amplitude and frequency of adjacent harmonic and interharmonic components. This work is supported by the Natural Science Foundation of Shaanxi Province (No. 2021JM-393).