In this paper, we apply quantum Hamilton mechanics to describe the dynamical motion of an electronic Cooper pair tunneling through a Josephson junction. Quantum Hamilton equations provide us a set of canonical equations q = f(q, p) and = g(q, p) to model the tunneling dynamics of a Cooper pair. Instead of using the conventional probabilistic description, we solve complex quantum trajectory q(t) = qR + qI·i from the Hamilton equations to demonstrate the tunneling dynamics on a geometrical phase plane. In order to control the dynamics of a cooper pair, we add a gate voltage parameter ng to the quantum Hamiltonian. By adjusting the magnitude of ng, we successfully control the tunneling dynamic of the Cooper pair such that the predicted current-voltage relation is in excellent agreement with the experimental measurements.