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A neural network approach (NNA) was proposed for estimating accurately harmonics and inter-harmonics parameters from the signals in power systems. It is aimed at the system in which the sampling frequency cannot be locked on the actual fundamental frequency. By training the frequencies, magnitudes and phases of the fundamental wave, the harmonics and the inter-harmonics based on the NNA, an accurate harmonics and inter-harmonics measurement result can be obtained as the algorithm converge. The simulating result shows that the estimated harmonics and inter-harmonics parameters can be measured at accuracy of 99.995% under actual fundamental frequency varying from 49.5 to 50.5 Hz.