Skeletal elements of living organisms (bones, teeth, horns, frustules of diatomic algae, mollusk shells, sea urchin needles, and sponge spicules) are biogenic composite materials consisting of an inorganic part (calcium phosphate and carbonate, silica) and various organic compounds. The first step in the synthesis of these materials is the condensation of an inorganic precursor under the control of biopolymers capable of interacting with the growing inorganic particle. We studied formation of calcium carbonate in the presence of copolymers of acrylic acid, 1‐vinylimidazole and vinylamine. Some of the copolymers were new, so their acid–base properties were characterized. The polymers have an influence on the precipitation of CaCO3 in aqueous medium, and depending on the polymer structure and the polymer‐calcium ratio, composite precipitates or stable dispersions were obtained. Composite nanoparticles have a negative charge, and they can interact with polymer bases to form calcium‐organic composite materials. Calcium carbonate formation under the control of organic polymers is a chemical model of calcium skeletal growth in living nature. The resulting composites containing micrometer‐range CaCO3 particles are promising materials for the design of microstructured coatings with a high surface density of functional groups. Some of the polymers studied are not involved in the resulting material, but affect the morphology of CaCO3, forming particles in the micrometer range, which are promising as fillers for plastics.