Abstract: Let the strong product graph of path P_m and star graph S_1,n-1 be G=P_m*S_1,n-1. Firstly, by inducing assumptions and constructing internally vertex or edge disjoint paths, combined with the centrality of star graph, the vertex fault diameter D_w(G) and edge fault diameter D′_t(G) of the graph G were given. The results show that for any vertex or edge fault in the graph G, there holds D_w(G)≤d(G)+2 and D′_t(G)≤d(G)+1. Secondly, through the unequal relation between the number of vertices and the number of edges, the upper bound of the vertex fault diameter of the strong product graph of two maximally connected graphs and the 
upper bound of the edge fault diameter of the strong product graph of two nontrivial connected graph were given.

Key words: path, star graph, strong product graph, vertex fault diameter, edge fault diameter