We introduce a new family of continuous distributions called the beta transmuted-H family which extends the transmuted family pioneered by Shaw and Buckley [34]. Some of its mathematical properties including explicit expressions for the ordinary moments, quantiles, generating functions and order statistics are derived. Some special models of the new family are provided. The maximum likelihood method is used for estimating the model parameters, and the finite sample performance of the estimators is assessed by simulation. The importance and flexibility of the proposed family are illustrated by applications to two real data sets.