The context tree models are widely used in a lot of research fields. Patricia like trees are applied to the context trees that are expanded according to the increase of the length of a source sequence in the previous researches of non-predictive source coding and model selection. The space complexity of the Patricia like context trees are O(t) where t is the length of a source sequence. On the other hand, the predictive Bayes source coding algorithm cannot use a Patricia like context tree, because it is difficult to hold and update the posterior probability parameters on a Patricia like tree. So the space complexity of the expanded trees in the predictive Bayes coding algorithm is O(t2). In this paper, we propose an efficient predictive Bayes coding algorithm using a new representation of the posterior probability parameters and the compact context tree holding the parameters whose space complexity is O(t).