We developed a transportable Linnik-type full-field low-coherent quantitative phase microscope that is able to compensate for optical path length (OPL) disturbance due to environmental mechanical noises. Though two-beam interferometers such as Linnik ones suffer from unstable OPL difference, we overcame this problem with a mechanical feedback system based on digital signal-processing that controls the OPL difference in sub-nanometer resolution precisely with a feedback bandwidth of 4 kHz. The developed setup has a footprint of 200 mm by 200 mm, a height of 500 mm, and a weight of 4.5 kilograms. In the transmission imaging mode, cells were cultured on a reflection-enhanced glass-bottom dish, and we obtained interference images sequentially while performing stepwise quarter-wavelength phase-shifting. Real-time image processing, including retrieval of the unwrapped phase from interference images and its background correction, along with the acquisition of interference images, was performed on a laptop computer. Emulation of the phase contrast (PhC) images and the differential interference contrast (DIC) images was also performed in real time. Moreover, our setup was applied for full-field cell membrane imaging in the reflection mode, where the cells were cultured on an anti-reflection (AR)-coated glass-bottom dish. The phase and intensity of the light reflected by the membrane revealed the outer shape of the cells independent of the refractive index. In this paper, we show imaging results on cultured cells in both transmission and reflection modes.