An enhanced first-order shear deformation theory (EFSDT) is developed for linear viscoelastic analysis of laminated composite and sandwich plates. Improved strain energy expression of the conventional Reissner/Mindlin first-order shear deformation theory (FSDT) through strain energy transformation is derived in the Laplace domain by minimizing the strain energy difference between FSDT and an efficient higher-order zigzag theory (EHOPT). The convolution theorem of Laplace transformation is applied to circumvent the complexity of dealing with linear viscoelastic materials. The present EFSDT with the Laplace domain approach has the same computational advantage of the conventional FSDT while improving upon the accuracy of the viscoelastic response by utilizing the postprocess recovery procedure. The accuracy and efficiency of the proposed theory are demonstrated through the numerical results obtained herein by comparing to those available in the open literature.