Entangled photons are the fundamental resource in quantum information processing. How to produce them efficiently has always been a matter of concern. Here we propose a new way to produce correlated photons efficiently from monolayer WS2 based on bound states in the continuum (BICs). The BICs of radiation modes in the monolayer WS2 are realized by designing the photonic crystal slab-WS2-slab structure. The generation efficiency of correlated photon pairs from such a structure has been studied by using a rigorous quantum model of spontaneous parametric down-conversion with the plane wave expansion method. It is found that the generation efficiency of correlated photon pairs is greatly improved if the signal and idler fields are located at the BICs determined by the inverse scattering matrix of the structure. This is in contrast to the parametric down-conversion process for the enhanced generation of nonlinear waves if the pump field is located at the BICs determined by the scattering matrix of the structure. The generation rate of the correlated photon pairs can be improved by 7 orders of magnitude in some designed structures. The generated quantum signals are sensitive to the wavelength and exhibit narrowed relative line width, which is very beneficial for quantum information processing.