Abstract: As the development of 3D print technology makes the manufacturing of complex graded structures more easily, it is necessary to carrying out the investigations with respect to the solving for complex graded problems. Now, the investigations about the problems that the modulus of beam structures varying along the axial direction or thickness direction grade are already more, while the investigations about the modulus varying along two directions synchronously are less. Thus a graded composite plane beam with modulus changed in exponential form synchronously along thickness direction and axial direction was investigated by using Fourier decomposition in complex form. The general solutions for four-order differential governing equation with variable coefficients were solved firstly by using semi-inverse method of elasticity. Then, the particular solution of the beam subjected to symmetric load effects was derived by series expansions. Finally, the correctness of series solutions was verified by comparing with finite element results. The results show that when the gradient varying in bi-directions, the stress distribution and deformation situations of the beam structure become more complex, that the stress is larger at the region with higher modulus, while the stress is smaller at the region with lower modulus. The series solutions proposed could be also extended to the investigation of other relevant plane or semi-plane inhomogeneous problem with graded varying in bi-directions.