This paper introduces a novel path planning method under non-holonomic constraint for car-like vehicles, which associates map discovery and heuristic search to attain an optimal resultant path. The map discovery applies fast marching method to investigate the map geometric information. After that, the support vector machine is performed to find obstacle clearance information. This information is then used as a heuristic function which helps greatly reduce the search space. The fast marching is performed again, guided by this function to generate vehicle motions under kinematic constraints. Experimental results have shown that this method is able to generate motions for non-holonomic vehicles. In comparison with related methods, the path generated by proposed method is smoother and stay farther away from the obstacles.