For optimization of the waveguide in an InGaN/GaN/AlGaN laser diode (LD) on a sapphire substrate, we solved the wave equation of the InGaN/GaN/AlGaN waveguide. Several guided modes in the LD waveguide have been presented and we have shown that an anti-crossing effect between the guided modes is an important phenomenon to understand the complicated behaviour of the modes in the LD waveguide under the variation of structure parameters. By systematically varying the widths of the waveguides of the LD waveguide, we can obtain a useful design category to obtain a high optical confinement factor and a low absorption coefficient for high performance of the LD on a sapphire substrate. (C) 2015 Elsevier B.V. All rights reserved.