In order to deal with the problem of modal analysis of the single-link manipulator with end-effector payload, an integral equation is used to express the bending moment of the single-link manipulator with end-effector payload by using the method of materials mechanics. Then the integral equation is transformed into a partial differential equation that has the same expression and different boundary conditions as Euler-Bernoulli equation. The mode functions can be obtained by solving the partial differential equation. As the parameter of the mode functions, natural frequency of the single-link manipulator with end-effector payload is expressed by an equation. An iterative method to solve the natural frequency from the equation and an approximate expression of the natural frequency are given. The comparison result of real values and approximate values of the natural frequencies shows that the errors do not exceed 10-4 except the first natural frequency, and the errors are close to zero with the increase of the natural frequency ordinal.