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This paper builds a field model of induction coil gun based on finite-element and boundary-element coupling method (FE-BECM). The fundamental of FE-BECM is introduced, and it is used in open-boundary eddy-current problem to prove its validity and find a way to reduce a nonconforming error. In the coil gun's FE-BECM model, the coil and projectile are discretized by finite elements; boundary elements are used to discretize the free space and associate unconnected finite-element regions. In FE-BECM model, the coordinates of nodes that belong to moving bodies change when movement occurs. The distribution of magnetic flux density and eddy current during the launch process is displayed. The result of FE-BECM is compared with experimental data and results of other numerical methods.