This paper presents a simple, cost-efficient, and highly stable quantitative differential phase-contrast (PC) microscopy based on Talbot interferometry. The proposed system is composed of an optical microscope coupled with a pair of Ronchi amplitude gratings that utilizes a light-emitting diode as a low temporal coherence light source. The quantitative differential PC images of the microscopic transparent samples are reconstructed by analyzing the deformation of moiré patterns using a phase-shifting procedure. Low temporal coherence leads to eliminating speckle noise and undesirable interferences to obtain high-quality images. The spatial phase stability of the system is investigated and compared to two other common-path interferometers. Additionally, the performance of the method is verified by the experimental results of a standard resolution test target and phase biological samples.