The normal distribution is the most important model in statistics for analysisof continuous data. We propose a new distribution, called the extended mixture normaldistribution, based on a linear mixture model. We obtain explicit expressions for theordinary and incomplete moments, generating and quantile functions, mean deviations andtwo measures of entropy. The method of maximum likelihood and Bayesian are adopted toestimate the model parameters. The proposed distribution can provide better fits to realdata than the normal and other classical distributions as shown by means of one application.