Removal of soluble organic and inorganic contaminants from wastewater to produce clean water has received much attention recently. However, the simultaneous enhancement of water permeability and removal efficiency is still a challenge for filtration membranes. Here, we present a new kind of nanocomposite paper (CSH/CNF) consisting of calcium silicate hydrate (CSH) nanosheets and cellulose nanofibers (CNFs), and demonstrate the rapid water filtration and highly efficient contaminant (e.g., dyes, proteins, and metal ions) adsorption properties. The CNFs can serve as the bridging material to connect the CSH nanosheets to form a porous network structure and vital channels in the CSH/CNF paper for rapid water transportation. The weight ratio of CSH nanosheets in the paper is up to 75–85%. The weight ratio of CSH nanosheets has a significant effect on the water permeability and removal efficiency. The water permeability of the CSH/CNF paper with 82.5 wt% CSH nanosheets reaches as high as 312.7 L m−2 h−1 bar−1, which is about 14.7 times that of the CSH/CNF paper with 75 wt% CSH nanosheets. Because of the high specific surface area and abundant adsorption sites of CSH nanosheets, the CSH/CNF paper with 82.5 wt% CSH nanosheets exhibits high adsorption capacities and removal efficiencies for methyl blue (242.6 mg g−1, 97.3%), bovine serum albumin (289.2 mg g−1, 98.5%) and Pb2+ ions (366.2 mg g−1, 98.2%). The CSH/CNF nanocomposite paper holds great potential for application in environmental wastewater purification.