Photonic time-stretch (PTS) has been extensively studied due to its great potential in analog-to-digital converters. Here, we propose and demonstrate a PTS system based on phase modulation for sub-octave applications. Different from the PTS system using a Mach-Zehnder modulator (MZM), the PTS system, which uses a phase modulator (PM), has an operation bandwidth within an octave and is more suitable for preprocessing of sub-octave signals. Within the sub-octave band, the system is free of all second-order spurious signals. Because there is no direct current bias in a PM, the problem of bias drift, as well as the nonlinear distortion caused by it, can be thoroughly avoided. In addition, based on phase modulation and direct detection, the proposed PTS system has higher stability and a more simplified structure than that based on coherent detection. An exact analytical model has been established, and some compact expressions have been derived to fully characterize all frequency components of the PM-based PTS system. System properties, including the power transfer function, 3-dB bandwidth, and nonlinear distortion have been discussed, and numerical and experimental results on the performance of the PM-based PTS have been presented. In addition, a dual-channel PTS that employs a PM and a push-pull MZM has been proposed to extend the operation bandwidth to multi-octave.