Interval-valued　data,　as　typical　symbolic　data,　provide　a　feasible　way　to　deal　with　massive　data　sets.　Although　a　lot　of　literature　has　been　focused　on　researching　interval-valued　regression　models,　few　works　are　devoted　to　exploring　Bayesian　methods　for　interval-valued　data.　In　this　paper,　we　propose　a　novel　Bayesian　parametrized　method　for　interval-valued　data　by　transforming　an　interval　into　a　reference　point,　and　further　establish　a　Bayesian　linear　regression　model.　The　advantage　of　the　Bayesian　parametrized　method　is　to　make　use　of　full　information　within　intervals　and　meanwhile　it　can　solve　the　potential　problem　of　multicollinearity　in　the　parametrized　method.　We　assume　the　prior　distribution　is　normal　with　zero　mean,　and　employ　the　EM　algorithm　to　obtain　the　empirical　Bayes　estimates.　The　results　of　experimental　and　real　data　sets　show　that　the　Bayesian　parametrized　method　has　a　superior　forecasting　advantage　when　the　sample　size　is　small　and　the　random　error　is　large.