Fire-fighting robot is still one of the fields in robotic competitions held these days. This paper is aimed to see the implementation of the Markov Decision Planning (MDP) problem in a fire-fighting robot's navigation. The MDP algorithm evolves planning of the actions the robot should take according to the policy. This planning is mapped into a grid map. Yet in the implementation, this planning is applied in a continuous map. Using a fire-fighting robot the succession of this planning implementation is undertaken. The result shows that the implementation of grid mapped in a continuous map yields significant impacts that lead the MDP to be able to solve the limitation of wall following algorithm. This algorithm is also applied in the real autonomous mobile robot.