Michelson interferometer can be applied to not only the building block of the fundamental research of physics, but also the precise measurement, such as the direct observation of gravity wave signal. Therefore, high performance Michelson interferometer is the key step towards the implementation of direct observation of weak gravity wave signal. Recently, the vacuum noise was reduced by injecting squeezed vacuum into the unused port of Michelson interferomter, and the phase signal optical field in Mach-Zender interferometer is amplified based on the four-wave mixing in hot Rubidium atom. Here we study high sensitivity quantum Michelson interferometer. In the Michelson interferometer, the linear optical beam splitter is replaced by a non-degenerated optical parametric amplifier to realize the splitting and combining of optical fields, and the squeezed vacuum is also injected into the unused port of interferomter, so that the high signal-to-noise ratio and high sensitivity of phase measurement can be realized. Due to the inevitable optical losses, the losses inside and outside the Michelson interferometer are considered in our theoretical model. We investigate the influences of the losses inside and outside the Michelson interferometer on the sensitivity of phase measurement. By theoretical calculation, we analyze the dependence of sensitivity of phase measurement on system parameters, such as intensity of optical fields for phase sensing, gain factor of non-degenerated optical parametric amplifier, the losses inside and outside the Michelson interferometer, and the squeezing parameter of input squeezed vacuum, and thus the condition of high sensitivity nonlinear Michelson interferometer can be obtained. In a broad system parametric range, the quantum Michaleson interferometer can surpass standard quantum limit, and the nonlinear Michaleson interferometer with squeezed state injection can provide the optimal sensitivity for phase measurement. The nonlinear Michelson interferometer with squeezed state is suitable for weak signal measurement. While the gain factor of non-degenerated optical parametric amplifier is large enough, the nonlinear Michelson interferometer without injecting the squeezed vacuum can still reach the optimal sensitivity, which reduces the use of quantum resources. When the phase sensing optical field is strong, the linear Michelson interferometer with injecting the squeezed vacuum can also reach the optimal sensitivity, and the sensitivity is robust for both losses inside and outside the interferometer. All the kinds of interferometers are more sensitive to the loss inside the interferometer than outside the interferometer, and the sensitivity of phase measurement can be improved by reducing the loss inside the interferometer. Our result provides direct reference of experimental implementation of high performance interferometer for high precision quantum metrology.