Supertagging is an important technique for deep syntactic analysis. A supertagger is usually trained independently of the parser using a sequence labeling method. This presents an inconsistent training objective between the supertagger and the parser. In this paper, we propose a forest-guided supertagger training method to alleviate this problem by incorporating global grammar constraints into the supertagging process using a CFGfilter. It also provides an approach to make the supertagger and the parser more tightly integrated. The experiment shows that using the forest-guided trained supertagger, the parser got an absolute 0.68% improvement from baseline in F-score for predicate-argument relation recognition accuracy and achieved a competitive result of 89.31% with a faster parsing speed, compared to a state-of-the-art HPSG parser.