Finite Mixture model has been studied for a long time, however, traditional methods assume that the variables are measured without error. Mixtures-of-regression model with measurement error imposes challenges to the statisticians, since both the mixture structure and the existence of measurement error can lead to inconsistent estimate for the regression coefficients. In order to solve the inconsistency, We propose series of methods to estimate the mixture likelihood of the mixtures-of-regressions model when there is measurement error, both in the responses and predictors. Different estimators of the parameters are derived and compared with respect to their relative efficiencies. The simulation results show that the proposed estimation methods work well and improve the estimating process.