Abstract: In recent yours there appeared an abuildancy of excellent results in the study of circular graphs wher'as little is done for the study of circular weighted graphs, especially of multipl'e circular weighted graphs and generalized circular weighted graphs. In this paper a spectral analysis for circular weighted graphs is done and a Spectrum theorem and a limit distribution theorem are given.The results obtained here are appllicable to the study of crystal energy spectrum, bomologue energy spectrum,uniform -continuous dielectric finite elements,etc.