Out-of-step oscillation is a serious physical phenomenon in the power system, which needs timely control and protection. However, this process requires accurate wide-area measurement information from PMU as a guarantee. This article firstly analyzes and illustrates the fact that the amplitude and frequency of bus voltage and system current fluctuate greatly during the out-of-step oscillation process, and points out the urgent demand to develop a novel suitable phasor measurement method under this condition. Then this article takes advantage of the 90 degree non-attenuation rotation characteristic of Hilbert transform, analyzes the error caused by discrete Hilbert transform, and gives the corresponding error elimination scheme to form a novel Hilbert translation based phasor measurement method. Through experiments, its advantages over the traditional DFT and Taylor series based phasor measurement methods are described in detail. It can be used as an important supplement to the PMU, which could provide the necessary accurate measurement information for out-of-step protection and control.