We present an accelerated variant of the constrained gentlest ascent dynamics (CGAD) for computing excited states of Bose-Einstein condensates within Gross-Pitaevskii theory. The traditional CGAD method, which is derived from the $L^2$-gradient flow, often converges slowly near the target constrained saddle points corresponding to excited states. By incorporating Sobolev gradients and inertial dynamics, the proposed method significantly improves the convergence rate. Numerical examples demonstrate the efficiency of the accelerated dynamics and show interesting excited states.