Tensor renormalization group (TRG) approach is a variant of the real-space renormalization group to evaluate the path integral in the thermodynamic limit, without resorting to any probabilistic interpretation for the given Boltzmann weight. Moreover, since the TRG can directly deal with the Grassmann variables, this approach can be formulated in the same manner for the systems with bosons, fermions, or both of them. These advantages of the TRG approach have been confirmed by the earlier studies of various lattice theories, which suggest that the TRG potentially enables us to investigate the parameter regimes where it is difficult to access with the standard stochastic numerical methods, such as the Monte Carlo simulation. In this talk, we explain recent our numerical study of the (1+1)-dimensional Hubbard model with the TRG approach. Our results of the critical chemical potential and the critical exponent ν are consistent with the exact solutions obtained by the Bethe Ansatz. This talk is based on arXiv:2105.00372.