Recent studies show that the pore network of unconventional rocks generally consists of inorganic and organic parts, forming a dual-wet medium. The organic part has high wetting affinity to oleic phase but low wetting affinity to aqueous phase. In contrast, the inorganic part has high wetting affinity to both oleic and aqueous phases. The objective of this study is to estimate the organic and inorganic pore size distributions (PSDs) of the unconventional rocks by analyzing the comparative oil and brine imbibition data. A previously-proposed fractal model which considers the non-piston-like imbibition front is used to achieve this objective. We use a history matching technique to fit the measured imbibition data with the proposed fractal model, and determine unknown parameters such as fractal dimension (FD), minimum pore diameter (D-min), and tortuosity (tau) that control the imbibition profile. The determined parameters are then used to estimate PSD. The PSD of inorganic and organic pores (PSDinorg+org) is calculated by oil imbibition data and the PSD of inorganic pores (PSDinorg) is calculated by brine imbibition data. The PSD of organic pores (PSDorg) is calculated by decoupling of PSDinorg+org and PSDinorg. Comparing the estimated PSDorg and PSDinorg shows that organic pores are generally smaller than inorganic pores, consistent with the results of scanning electron microscopy (SEM) and energy-dispersive X-ray spectroscopy (EDS) analyses, indicating the abundance of nanopores within the organic matter. Moreover, compared with the PSD from mercury injection capillary pressure (MICP) test, PSD estimated by oil imbibition shows very small pores (< 3 nm in diameter) which are not accessible by mercury, especially for the low-permeability rock samples. The method proposed in this study can complement the conventional MICP technique for a more comprehensive characterization of the pore network of unconventional rocks with dual-wet pore network.