The design features of light-emitting-diode heterostructures with a monolithic InGaN/GaN active region containing several InGaN quantum wells (QWs) emitting at different wavelengths, grown by metal-organic chemical vapor deposition, are studied. It is shown that the number of emission bands can be raised to three by increasing the number of deposited InGaN QWs with different indium contents. The emission efficiency decreases by approximately 30% with increasing number of QWs at high currents. The dependences of the optical properties of the heterostructures on the number of QWs and types of barriers between the QWs (GaN layer or InGaN/GaN short-period superlattice) are analyzed. It is demonstrated that the ratio between the intensities of the emission lines widely varies with current flowing through the structure and greatly depends on the type and width of the barriers between the QWs.