In order to avoid weight offset and improve the convergence speed, this paper presents the harmonic detection algorithm based on linearly constrained least mean square, although the least mean square algorithm has been widely used in the field of harmonic detection because of its low computational complexity and good stability. New algorithm adds a linear constraint condition of the weight variable. The amplitude and phase of a power signal containing harmonics and inter-harmonics are estimated using this algorithm in the presence of white Gaussian noise under simulating environment. Finally, the algorithm is tested under the steady-state signal, the dynamic signal and the arc furnace model. According to experimental results, this algorithm can detect the information of harmonics quickly and accurately in different environments, and it has faster convergence speed and higher anti-interference ability compared with the LMS algorithm. This work is supported by National Natural Science Foundation for Young Scholars (No. 51505317) and Natural Science Foundation of Shanxi Province (No. 201601D102039).