In recent years, based on jointly modeling the mean and variance, double regression models are widely used in practice. In order to assess the effects of continuous covariates or of time scales in a flexible way, a class of semiparametric mixed-effects double regression models(SMMEDRMs) is considered, in which we model the variance of the mixed effects directly as a function of the explanatory variables. In this paper, we propose a fully Bayesian inference for SMMEDRMs on the basis of B-spline estimates of nonparametric components. A computational efficient MCMC method which combines the Gibbs sampler and Metropolis-Hastings algorithm is implemented to simultaneously obtain the Bayesian estimates of unknown parameters and the smoothing function, as well as their standard deviation estimates. Finally, some simulation studies and a real example are used to illustrate the proposed methodology.