Nowadays, nanofiltration is widely used for water treatment due to its advantages, such as energy-saving, sustainability, high efficiency, and compact equipment. In the present work, novel nanofiltration membranes based on the polymer of intrinsic microporosity PIM-1 modified by metal-organic frameworks (MOFs)—MIL-140A and MIL-125—were developed to increase nanofiltration efficiency for the removal of heavy metal ions and dyes. The structural and physicochemical properties of the developed PIM-1 and PIM-1/MOFs membranes were studied by the spectroscopic technique (FTIR), microscopic methods (SEM and AFM), and contact angle measurement. Transport properties of the developed PIM-1 and PIM-1/MOFs membranes were evaluated in the nanofiltration of the model and real mixtures containing food dyes and heavy metal ions. It was found that the introduction of MOFs (MIL-140A and MIL-125) led to an increase in membrane permeability. It was demonstrated that the membranes could be used to remove and concentrate the food dyes and heavy metal ions from model and real mixtures.