  We apply the Grassmann tensor renormalization group to the lattice
regularized Schwinger model with one-flavor of the Wilson fermion. We study the
phase diagram in the $(\beta,\kappa)$ plane performing a detailed analysis of
the scaling behavior of the Lee-Yang zeros and the peak height of the chiral
susceptibility. Our results strongly indicate that the whole range of the phase
transition line starting from $(\beta,\kappa)=(0.0,0.380665(59))$ and ending at
$(\infty,0.25)$ belongs to the two-dimensional Ising universality class
similarly to the free fermion case.
