The applications of physics-informed neural networks (PINNs) in material parameters identification of composite laminates are currently research highlights. We present an efficient physics-constrained deep learning approach based on PINNs for solving material parameters of composite laminates. We explain the details of incorporating first-order shear deformation theory as physical information into designed loss functions. The performance of proposed approach is demonstrated through a numerical example of idealized composite laminated plates under uniform pressure conditions. The computational errors of material parameters are less than 0.1%. Moreover, the applicability of transfer learning (TL) has been illustrated for inversion of material parameters with few datasets. The ambition is to improve the identification efficiency of carbon and glass fiber reinforced plies material parameters across various loading conditions. Intensive studies are conducted to compare convergence time between with and without TL through a numerical example under thermal-force coupling conditions. The comparison shows PINNs with TL obtain average error of 0.144% and 0.077% in carbon and glass fiber reinforced plies, which is better than without TL of 0.472% and 0.284%, respectively. The proposed work emphasizes the effective application of PINNs-based approach that combines first-order deformation and data-driven solution features for inverse solving material parameters of composite laminates.