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 dou-ble-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 charac-ters: 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 pre-sented.