We introduce a new family of continuous distributions called the transmuted geometric-G family which extends the transmuted family pioneered by Shaw and Buckley (2007). Some of its mathematical properties including explicit expressions for the ordinary and incomplete moments, generating function, Rényi and Shannon entropies, order statistics and probability weighted moments are derived. Some special models of the new family are provided. The maximum likelihood method is used for estimating the model parameters. The importance and flexibility of the proposed family are illustrated by two applications to real data sets.