Abstract: A micromechanics model was developed to characterize the effective creep response and macroscopic stress-strain behavior of linear viscoelastic polymer matrix composites based on variational asymptotic homogenization theory framework. Stated from the energy functional variational expression derived from the constitutive equations of the linear viscoelastic polymer matrix composites, the effective creep compliance coefficients of the linear viscoelastic polymer matrix composites were solved by using the variational asymptotic method. On this basis, the time-dependent and uniaxial tensile behavior of polymer matrix composites were calculated. The applicability and accuracy of the model were verified by numerical examples. Since all calculations were accomplished in the time domain, the Laplace transform and inversion commonly used for linearly viscoelastic composites are not needed in this theory, and the computational efficiency is greatly improved.