Large and complex structures such as ship panels generally have various types of welding-induced distortions including angular deformation, longitudinal bending, and buckling. Developing efficient methodologies for modeling welding distortions and residual stresses of large structures plays a critical role in industrial applications. Conventional transient moving source analyses on three-dimensional (3D) finite element models, where millions of degrees of freedom and thousands of time increments are involved, demonstrate the capability to capture all types of welding distortions, but proved to be computational costly. The 2D to 3D applied plastic strain method, where only longitudinal plastic strain resulting from 2D models is mapped to a 3D structural model, successfully predicts buckling and bowing distortions. However, it cannot calculate angular distortion accurately. In this paper, a 3D applied plastic strain method has been developed to predict the welding distortions for structures. In the applied strain method, six components of the plastic strain of each weld are calculated by performing a 3D moving source analysis on a small 3D model with a shorter length, then the plastic strain components of the small models are mapped and superposed to a large 3D structural model to obtain the final distortion results. An interpolation algorithm is developed for mapping between meshes with different densities. The effectiveness of the 3D applied plastic strain method is evaluated by comparing to the distortion results from 3D moving source simulations. The mapping algorithm is verified and the effects of the model size on the distortion results are investigated. The numerical results show that the applied plastic strain method accounts all distortion modes, but is only qualitatively accurate for the prediction of angular distortion.