Aiming at the estimation problem of the mixed effect model when longitudinal data obey non-normal distribution a Bayesian estimation method of semi-parametric mixed effect model with skew-normal distribution was proposed. Individual measurement error obeys skew-normal distribution and the relationship between longitudinal index and time was modeled by B spline method. Bayesian analysis of the model was considered under conjugate prior and Bayesian estimation of unknown parameters random effects and nonparametric functions was obtained based on the mixed algorithm of MH algorithm and Gibbs sampling. In the numerical simulation under the condition of non-normal distribution of data the estimation obtained by the skew-normal method was compared with that of the traditional semi parametric mixed effect model. It is found that the skew-normal semiparametric mixed effect model performs better under the condition of limited samples which indicates that the skew-normal semiparametric mixed effect model can better fit the skewed data than the traditional model and the Bayesian method can effectively use prior information to obtain more accurate parameter estimation. Finally the modified method was applied to ADNI data and the relationship between neural score and baseline clinical indicators was studied. A reasonable conclusion was drawn which proved the rationality of the method.