Abstract: The dispersive property of layered periodic composites structure was researched by improved global matrix approach, firstly. It was found that the structure represented characterization of the homogenous anisotropic materials when the number of layer was large enough. Then the effective modules algorithm was developed and its applicability was discussed. The effective modules could be accepted in two ranges including the lower frequency band as well as the higher frequency and phase velocity band. However, the dispersive curves could not be calculated using effective modules in situation of higher frequency band with lower phase velocity below the longitudinal wave velocity, and the characterization of waves needed further investigation.