The modified-half-normal distribution often occurs as one of the posterior conditionals in many Bayesian statistical models. In order to developa uniformly efficient random variate generator for the entire parameter range of such distribution, we propose a relaxed transformed density rejection method such that it is available in case the optimal contact points in the original transformed density rejection method have no closed-form. Simulation results verify that the resultant generator is fast and robust for various distribution parameters. The proposed generator is particularly suitable for the varying parameter case such as in Gibbs sampler.