To provide an accurate phasor reference value for the performance analysis of a synchronous phasor measurement unit (PMU) running on site and to ensure its data quality, a high-precision phasor measurement method based on orthogonal polynomial fitting is proposed. This method uses the orthogonality of Legendre polynomials to fit the signal model, so as to construct an orthogonal fitting phasor model. By analyzing and comparing the complexity of different fitting parameter solution methods, a phasor reference value calculation method based on Cholesky decomposition is proposed. This provides a new solution for the problem of a large amount of calculation of nonlinear fitting parameters, and ensures the measurement accuracy through iterative correction. Further, according to the optimal window length and fitting order revealed by the analysis, a high-precision measurement and efficient calculation of the algorithm are realized. The simulation and hardware test show that the measurement accuracy meets the standard requirements by a factor of 10 or more. It can run stably in real time on the hardware and provide reference values for PMU field test and calibration. This work is supported by the National Natural Science Foundation of China (No. 51627811 and No. 51725702).