In this work, a flexible class of linear mixed models is introduced by assuming that the random effects and model errors follow a skew-normal-Cauchy distribution. The likelihood function and the information matrix based on of the observed data are computed. An EM-type algorithm is also proposed for estimating the parameters that seems to provide some advantages over a direct maximization of the likelihood function. Finally, the performance of the proposed model is evaluated numerically from simulated an real data.