We present a construction method for reduced-order models (ROMs) to explore alternatives to numerical simulations. The proposed method can efficiently construct ROMs for non-linear problems with contact and impact behaviors by using tensor decomposition for factorizing multidimensional data and Akima-spline interpolation without tuning any parameters. First, we construct learning tensor data of nodal displacements or accelerations using finite element analysis with some representative parameter sets. Second, the data are decomposed into a set of mode matrices and one small core tensor using Tucker decomposition. Third, Akima-spline interpolation is applied to the mode matrices to predict values within the data range. Finally, the time history responses with new parameter sets are generated by multiplying the expanded mode matrices and small core tensor. The performance of the proposed method is studied by constructing ROMs for airbag impact simulations based on limited learning data. The proposed ROMs can accurately predict airbag deployment behavior even for new parameter sets using the Akima-spline interpolation scheme. Furthermore, an extremely high data compression ratio (more than 1000) and efficient predictions of the response surfaces and Pareto frontier (2000 times faster than that of full finite element analyses using all parameter sets) can be realized.