Time-stretch technique has been researched for a long time and many implementations with different performance have been proposed. In this paper, we utilize phase modulation and optical coherent detection (PM-CD) to implement photonic time-stretch analog-to-digital converter. In this implementation scheme, only one optical source is used to ensure the coherence of the modulated signal and the reference signal. Besides, envelope removing technique is also employed to remove the Gaussian envelope contained in the stretched radio frequency (RF) signal. As a proof of its feasibility, this paper presents a brief analysis of the time-stretch technique and the implementation of the PM-CD system we proposed. A comprehensive mathematical model for the PM-CD combining with envelope removing technique is developed and a numerical simulation is also presented. Simulation results show this technique can not only slow down the high frequency RF signal but also recover the stretched RF signal with little distortion. The most important point is the phase error in PM-CD, the nonlinearity of the photodetector (PD) and the pulse-to-pulse variations can be eliminated at the same time. This technique is an improvement compared to the previously proposed PM-CD time-stretch analog-to-digital converter.