To analyze the characteristics of a power system transient signal and calculate its derivative, it is feasible to fit the function expression of the signal based on a sample, but the existing transient signal fitting methods still have shortcomings of certainty and derivability of the fitting function. Given this, a sinusoidal representation method for transient signal analysis of a power system based on a Hilbert transform is proposed. The sine function of the transient signal is used to form a fitting basis function, and the Hilbert transform is used to meet the certainty of the fitting function. Compared with the existing methods, this method can directly decompose the steady-state component and transient component of the fault transient signal, and its transient component can reflect the attenuation characteristics of the fault signal. This method can also fit the function expression of the transient signal, and then calculate the arbitrary order derivative value of the transient voltage and current signal. This is the basis of many signal processing calculations. Through the analysis of a set of given signals and a set of field recorded signals, the effectiveness of the proposed method is verified. This work is supported by the National Natural Science Foundation of China (No. 51877020).