As an extension of the generalized bead–rod model developed earlier by the authors, this paper proposes a method for Brownian dynamics simulations of charged semiflexible polymers confined to various curved surfaces such as spherical, cylindrical, ellipsoidal and toroidal. We model charged semiflexible polymers as discrete wormlike chains consisting of virtual beads connected by inextensible rods with length varying according to the characteristic radius of curvature of the confining surface. The long-range electrostatic interactions are incorporated via the Debye–Hueckel potential. The geometrical constraints associated with the inextensible rods are realized by the so-called linear constraint solver. For a semiflexible polymer chain confined to a spherical surface, an analytical expression for the winding number is obtained by using an existing exact closed-form solution of the mean-square end-to-end distance. The proposed simulation method is then validated against theoretical predictions for both charged and uncharged polymer chains under surface confinements.