Comets, the sporadic visitors from the outer edges of the Solar System, are considered to hold the key for understanding the formation of planets and the origin of life on Earth. Having spent the majority of time away from the radiative environment of the inner Solar System, the chemistry of the comets has remained unaltered, making them the pristine samples of the matter from the ancient Solar nebula. A mission to bring cometary particles back to Earth enables the examination of the materials in well equipped laboratories and saves the mass of the instruments to be carried on board. As conventional propulsion methods require a large quantity of propellant for this type of mission, the feasibility of using the novel propulsion technique of solar sailing is explored in this thesis. In order to return the comet samples to Earth within a reasonable time period, the orbit transfer is considered as an optimal control problem with constraints placed on the sailcraft’s position and velocity. The Differential Evolution (DE) algorithm was used to search for time-optimal trajectories that minimize the approach distance and the relative velocity with respect to the comet during sample collection. The optimal trajectory obtained predicts the solar sailcraft to reach the comet, collect the samples and return back to Earth in 6.8 years. The time of arrival at the comet was found to match with the comet's perihelion passage, enabling effective sample collection. The outcome of the trajectory analysis, thus successfully demonstrates the applicability of solar sailing to comet sample return missions in the near future.