The traditional estimation of mixture regression models is based on the normal assumption of component errors and thus is sensitive to outliers or heavy-tailed errors. A robust mixture regression model based on the t-distribution by extending the mixture of t-distributions to the regression setting is proposed. However, this proposed new mixture regression model is still not robust to high leverage outliers. In order to overcome this, a modified version of the proposed method, which fits the mixture regression based on the t-distribution to the data after adaptively trimming high leverage points, is also proposed. Furthermore, it is proposed to adaptively choose the degrees of freedom for the t-distribution using profile likelihood. The proposed robust mixture regression estimate has high efficiency due to the adaptive choice of degrees of freedom.