In recent years, increasing attention has been devoted to X-ray phase contrast imaging, since it can provide high-contrast images by using phase variations. Among the different existing techniques, Zernike phase contrast microscopy is one of the most popular phase-sensitive techniques for investigating the fine structure of the sample at high spatial resolution. In X-ray Zernike phase contrast microscopy, the image contrast is indeed a mixture of absorption and phase contrast. Therefore, this technique just provides qualitative information on the object, which makes the interpretation of the image difficult. In this contribution, an approach is proposed for quantitative phase retrieval in X-ray Zernike phase contrast microscopy. By shifting the phase of the direct light by pi/2 and 3 pi/2, two images of the same object are measured successively. The phase information of the object can then be quantitatively retrieved by a proper combination of the measured images. Numerical experiments were carried out and the results confirmed the feasibility of the proposed method. It is expected that the proposed method will find widespread applications in biology, materials science and so on.