Distortion prediction of a welded structure is an important way to improve work efficiency and ensure product quality during the fabrication process. Recently, the widely used approaches for evaluating residual deformation include the thermo-elastic-plastic finite element method (TEP-FEM) and the inherent strain method (ISM). The former can accurately simulate the entire welding process with excessive computational time, whereas the latter has great potential in the fast prediction of residual distortion in complex welded components. In this study, an equivalent thermal strain method based on inherent strain theory was proposed to predict residual deformation of the multi-seam welded pipe structures. Moreover, a full 3D TEP-FEM model was also developed to estimate the distributions of inherent strain in longitudinal (L-seam) and circumferential (C-seam) welds. To validate the accuracy of the proposed ISM, the welding distortion predicted by the proposed ISM is compared with the experimental data and TEP-FEM simulation results. It is discovered that the proposed ISM can be used to accurately predict welding-induced deformation in multi-seam welded pipe structures. Furthermore, compared with TEP-FEM simulation, the significant advantage of this approach is that the computing efficiency can be increased by about 50 times.