Metal-organic frameworks (MOFs) are a class of customizable porous material, which have shown good performance in separation processes, because of their large surface area and molecular recognition property. Although the effects of chemical structure of MOFs on their separation performance were extensively studied, the exploration of their surface properties was still limited. This work demonstrated a MOF nanosheet with large amount of coordinatively unsaturated metal sites, Cu(BDC) (copper(II) benzenedicarboxylate), where the unsaturated Cu sites were utilized to selectively adsorb organic molecules with Lewis basicity. This work also investigated the direct growth of Cu(BDC) on the cellulose substrate, where the MOF nanosheets were immobilized on the cellulose substrate, enabling the composite material for practical applications. The heterogeneous nucleation and growth of MOF nanosheets on the cellulose were achieved by tuning the basicity of solution and reaction temperature. We believe this direct growth approach can be applied to other MOF composite materials for separation and purification purposes, as well as other applications involving molecular recognition properties of MOFs, such as sensing, catalysis, and enzyme immobilization.