The Cox–Ingersoll–Ross model is widely used in financial engineering for the pricing of interest rate derivatives. Various Euler–Maruyama- and Milstein-type discretization schemes have been developed to approximate its solution, among which the full truncation Euler–Maruyama method is popular in practice and is known to be 𝒧^𝑝-strongly convergent with order 1/2 under certain parameter conditions. In this paper, we investigate the projected Euler–Maruyama method for solving the Cox–Ingersoll–Ross model. By combining the projection technique with the normalized error analysis introduced by Cozma and Reisinger, we establish the 𝒧^𝑝-strong convergence of the projected Euler–Maruyama method with order 1/2 over a significantly wide range of parameter settings.