We consider the Burgers'' type equation with a viscosity term and a time periodic force defined on a one dimensional open interval domain with Dirichlet boundary condition. We prove the existence of the time periodic solution with some regular time periodic force by using Galerkin method and Schaefer''s fixed point theorem, and moreover, we show that this time periodic solution is unique and globally asymptotically stable in $H^1$ sense under additional condition with small force in some sense.
