Abstract: A damage evolution law for linear viscoelastic unidirectional (UD) composites undergoing transverse matrix cracking has been proposed. Based on this model, the transverse tensile properties of the UD composites were predicted precisely. The damage evolution law was constructed using the Weibull distribution of defects which will develop into cracks as a result of deformation. The time-temperature superposition principle (TTSP) approach has been interpreted with physical basis through this damage evolution law. The whole process of using this damage model to predict the properties of a UD composite during deformation was demonstrated in this paper through an example of its application, and the results have been compared with experimental data. The transverse tensile behavior of UD composite can be predicted precisely by this model. In terms of failure and strength prediction, a noticeable discrepancy is present due to the brittleness of the transverse direction of UD composite.