Generally, the Terminal Based Navigation System(TBNS) used embedded road data searches a path that has less qualitative than The Center Based Navigation System(CBNS). TBNS has not used real time road data but it is recently able to use it with technique such as TPEG. However, it causes to increase a cost of exploring by using real time road data for improvement quality of a path, because of limited performance. In this paper, we propose a Dynamic Heuristic to improve quality of path in the TBNS. Dynamic Heuristic(DH) is not fixed data and is dynamically modified using transferred real time road data from server. In this paper, we propose path-lading algorithm with Maximum Speed Dynamic Heuristic (DH-MAX) and do an experiment. The DH-MAX is to be used the highest speed as DH, in real map divided by same size. And proposed algorithm searches path using the priority searching only of the fixed data, but also the highest speed with real time information. In the performance test, the quality of path is enhanced but the cost of searching is increased than A* algorithm.