  We apply the tensor renormalization group method to the (1+1)-dimensional
SU(2) principal chiral model at finite chemical potential with the use of the
Gauss-Legendre quadrature to discretize the SU(2) Lie group. The internal
energy at vanishing chemical potential $\mu=0$ shows good consistency with the
prediction of the strong and weak coupling expansions. This indicates an
effectiveness of the Gauss-Legendre quadrature for the partitioning of the
SU(2) Lie group. In the finite density region with $\mu\ne 0$ at the strong
coupling we observe the Silver-Blaze phenomenon for the number density.
