  We investigated the chiral symmetry and U_A(1) anomaly at finite temperature
by applying the functional renormalization group to the SU(3) linear sigma
model. Expanding the local potential around the classical fields, we derived
the flow equations for the renormalization parameters. In chiral limit, the
flow equation for the chiral condensate is decoupled from the others and can be
analytically solved. The Goldstone theorem is guaranteed in vacuum and at
finite temperature, and the two phase transitions for the chiral and U_A(1)
symmetry restoration happen at the same critical temperature. In general case
with explicit chiral symmetry breaking, the two symmetries are partially and
slowly restored, and the scalar and pseudoscalar meson masses are controlled by
the restoration in the limit of high temperature.
