One of the most promising ways to solve the problem of reducing the rate of depletion of natural non-renewable components of concrete is their complete or partial replacement with renewable plant counterparts that are industrial and agricultural waste. The research significance of this article lies in the determination at the micro- and macro-levels of the principles of the relationship between the composition, the process of structure formation and the formation of properties of concrete based on coconut shells (CSs), as well as the substantiation at the micro- and macro-levels of the effectiveness of such a solution from the point of view of fundamental and applied materials science. The aim of this study was to solve the problem of substantiating the feasibility of concrete consisting of a mineral cement–sand matrix and aggregate in the form of crushed CS, as well as finding a rational combination of components and studying the structure and characteristics of concrete. Test samples were manufactured with a partial substitution of natural coarse aggregate with CS in an amount from 0% to 30% in increments of 5% by volume. The following main characteristics have been studied: density, compressive strength, bending strength and prism strength. The study used regulatory testing and scanning electron microscopy. The density of concrete decreased to 9.1% with increasing the CS content to 30%. The highest values for the strength characteristics and coefficient of construction quality (CCQ) were recorded for concretes containing 5% CS: compressive strength—38.0 MPa, prism strength—28.9 MPa, bending strength—6.1 MPa and CCQ—0.01731 MPa × m3/kg. The increase in compressive strength was 4.1%, prismatic strength—4.0%, bending strength—3.4% and CCQ—6.1% compared with concrete without CS. Increasing the CS content from 10% to 30% inevitably led to a significant drop in the strength characteristics (up to 42%) compared with concrete without CS. Analysis of the microstructure of concrete containing CS instead of part of the natural coarse aggregate revealed that the cement paste penetrates into the pores of the CS, thereby creating good adhesion of this aggregate to the cement–sand matrix.