The transient response of a functionally graded strip with heat convection supply from the well-stirred fluid is analyzed. The fluid with heat sink loses heat to the functionally graded strip. The thermal conductivity and the heat capacity of the functionally graded strip vary continuously. The analytical solution is obtained by applying the Laplace transform and inverse Laplace transform theorem to the partial differential heat conduction equation in two cases. Numerical solution is also presented. The roots of transcendental equations are sensitive to graded parameters. An iterative algorithm is proposed to get the successive roots, and the computational accuracy in terms of the roots is demonstrated, which is greatly different from that in homogeneous materials. The temperature distributions in the thickness direction are shown. Influences of graded parameters and the thickness of the functionally graded strip on temperature distributions of both the functionally graded strip and the fluid are systematically studied, and are helpful for the design optimization and application of the graded materials.