This paper reports a finite element based numerical framework for simulating the electromechanical behavior of nonlinear anisotropic dielectric elastomer actuators at finite strains. Based on the existing models for incompressible anisotropic neo-Hookean hyperelastic solids and ideal dielectric elastomers, a theory of anisotropic dielectric elastomers is outlined. The analytical expressions are derived for the tangent moduli of the anisotropic materials. A computationally efficient staggered solution algorithm is presented for solving the coupled nonlinear equations by decoupling displacement and electric potential fields. Selective reduced integration technique is used for alleviating the volumetric locking due to material incompressibility. The model is implemented into an in-house finite element program. We first validate the accuracy of the finite element implementation by considering the cases of homogeneous deformation, with a particular emphasis on the electromechanical instability. Subsequently we demonstrate the utility of the proposed numerical framework by analyzing two representative cases (bending and buckling actuators) involving inhomogeneous deformations. In both the cases, anisotropy in the mechanical properties of the elastomer is found to have a favorable influence on the actuation performance. Finally, for various mesh sizes, a comparison of the computation time required by the monolithic solution approach and the proposed staggered approach is presented to highlight the computational efficacy of the latter. © 2018 Elsevier B.V.