A method of moving in a minimum cost path using a grid map, and an apparatus to perform the method, the method including calculating a move cost to a goal, from each of a plurality of cells comprises in a space in which a mobile home appliance moves, and planning a movement path to the goal according to the move cost; determining one or more via points at which a direction changes on the movement path; planning the minimum cost path from the movement path by selecting one or more shortest-distance via points from the via points; and moving from a first shortest-distance via point to a second shortest-distance via point.