We propose a new diffraction phase microscope (DPM), in which a photon counting (PC)-based single-pixel imaging (SPI) technique is introduced for obtaining two-dimensional quantitative phase images (QPIs) of transparent objects. The introduction of the SPI technique is promising for alleviating the sensitivity problem in DPM. This is because a highsensitive single-channel photodetector such as a photomultiplier tube can be used and the spatial multiplex advantage in the signal-to-noise ratio (SNR) can be expected. Furthermore, the employment of the PC technique solves the dynamic range problem inherent to the SPI. As a proof-of-principle experiment, we measured the QPI of a 125-nm thickness ITO layer coated on a silica-glass substrate, demonstrating the superiority of the PC-based SPI-DPM over SPI-DPM in SNR.