Wavelength assignment is one of the main algorithmic problems arising from WDM all optical networks, which is important in the theory and the practice. The wavelength assignment problem on optical rings with fixed wavelength converters is considered. First, two preprocess algorithms are designed to decompose a communication request set into some continuous cyclic sequences. Then the permutation group is used to represent the ring network with fixed converters and an algorithm is proposed to classify the wavelength channels into some groups.Based on these on these ideas,a wavelength assignment algorithm is presented.For an optical ring with any fixed conversion mode,the algorithm can giv a good assignment scheme.