A new method,step-search-diameter,to calculate the diameter of undirected double-loop networks G(N;±1,±s) was presented.A new diagram,spiral ring whose attributes were studied,was obtained by this method.A simple formula to express the d(N;±1,±s) of undirected double-loop networks was presented.The algorithm to calculate the diameter of undirected double-loop networks whose N,s were fixed and the algorithm to calculate the diameter of undirected double-loop networks whose N was fixed but s varied from 2 to N?1 were both given.VB6.0 and SQL Server 2000 were used to simulate the latter algorithm.The diameters of such family of undirected double-loop networks had such characters:maximum values,minimum values,symmetry.For any given N,many s made G(N;±1,±s) tight optimal or nearly tight optimal.The limited bound of diameter of undirected double-loop networks G(N;±1,±s) presented by Boesch and Wang is certified.A new formula to calculate the upper bound of the diameter of undirected double-loop networks is presented.