A new distribution, the gamma-half normal distribution, is proposed and studied. Various structural properties of the gamma-half normal distribution are derived. The shape of the distribution may be unimodal or bimodal. Results for moments, limit behavior, mean deviations and Shannon entropy are provided. To estimate the model parameters, the method of maximum likelihood estimation is proposed. Three real-life data sets are used to illustrate the applicability of the gamma-half normal distribution.