This work presents a new co-rotational beam element formulation to model the geometric three-dimensional static and dynamic nonlinear analysis of risers of Functionally Graded Materials (FGM). The material modulus of elasticity and density of the beam are assumed to vary through the pipe cross-section thickness following a power law function. In the spatial discretization of the riser equilibrium equations, a two node beam element based on Euler-Bernoulli theory is considered, with cubic Hermitian interpolation functions used for nodal displacement interpolations and element kinematics, all referred to a co-rotation coordinate system attached to the element local frame. In the element model, geometric non-linear effects are considered, involving large displacements and rotations but small strains. The motion of the riser results from the following applied forces: self weight, buoyancy, hydrodynamic (due to maritime waves, currents and added mass inertia), prescribed displacements (at the floating platform), action of floaters and seabed-structure interactions. Step-by-step time integration of the equilibrium equations is performed with HHT (Hilbert-Hughes- Taylor) algorithm and the numerical solution is obtained using the Newton- Raphson iterative technique. The methodology has been implemented and various sample results presented, that highlight the behavior of functionally graded material beams as compared to homogeneous beams. Applications related to practical offshore engineering situations are also considered.