Quantitative phase imaging (QPI), which combines phase imaging with optical microscopy technology, provides a marker-free, fast, non-destructive, and high-resolution imaging method for observing transparent biological samples. It is widely used in life science, biomedicine, etc. As an emerging QPI technology, spiral phase contrast microscopy (SPCM) uses a spiral phase filter to achieve edge enhancement of amplitude or phase objects. Using the multi-step phase-shifting technology, a complex sample can be measured quantitatively, which has the advantages of high stability, high sensitivity and high precision. However, the SPCM requires at least three-step phase-shifted spiral phase filtered images to achieve the quantitative reconstruction of the amplitude and phase of a sample, and the image acquisition process and the reconstruction process are relatively complicated, which require high stability of system, and the SPCM has low temporal resolution. In order to further improve the performance of SPCM and increase the system stability, sensitivity and temporal resolution, in this paper a quantitative phase imaging method and system based on a fractional spiral phase plate is proposed. Through a sample intensity image filtered by a fractional spiral phase plate, the modified Gerchberg-Saxton iterative phase retrieval algorithm is used to quantitatively reconstruct the phase of a pure phase sample, which simplifies the experimental process and phase reconstruction steps of spiral phase contrast microsocopy. In the computer simulation experiments, the phase imaging process and the reconstruction process of spiral phase plates based on different topological charges are studied, the feasibility of which is analyzed. Finally, through imaging and phase reconstruction of the phase grating and biological cell sample, it is verified that the phase contrast microscopy method based on the fractional spiral phase plate can effectively improve the contrast of spiral phase contrast microscopy and can obtain a quantitative reconstruciton of a weak phase object. The phase information of a sample has significance in research and application for developing the spiral phase contrast microscopy.