In this paper, the generalized differential quadrature (GDQ) method is presented for solving the nonlinear, fully intrinsic equations of geometrically exact rotating and nonrotating beams. The fully intrinsic equations of beams involve only moments, forces, velocity and angular velocity, and in these equations, the displacements and rotations will not appear explicitly. This paper presents the generalized differential quadrature method for solution of these equations. To show the accuracy, validity and applicability of the proposed generalized differential quadrature method for solving the fully intrinsic beam equations, different cases are considered. It is found that the GDQ method gives very accurate results with very few numbers of discrete points and also has very low computational cost as compared to some other conventional numerical methods and therefore this method is very efficient, accurate and fast for solving the fully intrinsic equations.