Abstract: The wide-distance and wide-diameter of a graph G containing disjoint paths between two vertices of G are studied. Some characterizes of the circulant graphs with order n and degree 4 are given by symmetry of the circulant graphs. Some upper and lower bounds of wide diameter of the circulant graphs of degree 4 are also obtained. The results can be used to measure the transmission delay and fault of a class of symmetric interconnection network which is modeled as a circulant graph.