In driving a car, turns such as left turns, right turns, or u-turns, make the speed of the car decrease considerably. A more straight path, therefore, is probably faster to arrive at the destination than zig-zag path with same distance. In this paper, we have newly proposed the turn heuristic to make more straight path. The path navigation algorithm with turn heuristic(called as TA* algorithm) could enhance the straightness of a path by putting the turned-edges to the turn cost. It requires higher cost to use TA* algorithm than traditional A* algorithm because the straight-edge first searching have increased the search space. We have improved the TA* algorithm into the variable TA* algorithm(called as VTA* algorithm) which adopt the turn-heuristic during the a portion of the whole path.