We propose a full Bayesian subset selection method for reproductive dispersion linear models, which bases on  expanding the
usual link function to a function that incorporates all possible  subsets of predictors by adding indictors as parameters. The vector of indicator variables
 dictates which predictors to delete.  An efficient MCMC  procedure that combing Gibbs sampler and Metropolis-Hastings algorithm is
presented to approximate the posterior distribution of the indicator variables. The promising subsets of predictors can be identified as
those with higher posterior probability. Several numerical examples are used to illustrate the newly developed methodology.