Using a variable-coefficient nonlinear Schrödinger equation, transmission profile of a single soliton in the optical fiber with an inhomogeneous region is studied numerically. It is found that the transmitted wave contains two solitons which form a bound state when the difference of the dispersion coefficient between the inhomogeneous and the homogeneous regions is large enough. When the amplitude of the transmitted wave is small, the transmitted wave is apt to contain a bound state soliton. With the increase of the length of the inhomogeneous region, a quantity E3, which is the conserved quantity of the constant-coefficient nonlinear Schrödinger equation, for the transmitted wave converges to an asymptotic value with oscillation. It is found that the nonsoliton wave part of E3 for the transmitted wave converges to an asymptotic value rapidly compared with other contributions to E3. We find the condition for the parameters of the inhomogeneous region that a stable soliton can exist on the entire fiber.