Abstract: Among the most fundamental tasks to be performed in grid systems are the construction of a breadth-first tree for the network rooted at a given source node, and the use of such a tree for performing broadcast and convergent communication. Presently all the breadth-first search algorithms are synchronous algorithms based on graph theory, and they are inapplicable in the asynchronous environment of grid systems. Although Lynch defines an asynchronous breadth-first search algorithm, the source node can’t detect the termination of this algorithm. So, this is not a true algorithm and inapplicable in practice. With the introduction of asynchronous automaton theory, an asynchronous grid breadth-first search algorithm, GridBFS algorithm is implemented. It is also proved that this algorithm will eventually produce a breadth-first tree, and the source node will detect the end of this algorithm.