This paper proposes the use of solar-sail technology currently under development at NASA Langley Research Center for a CubeSat rendezvous mission with asteroid 2016 HO 3 , a quasi-satellite of Earth. Time-optimal trajectories are sought for within a 2022–2023 launch window, starting from an assumed launcher ejection condition in the Earth-Moon system. The optimal control problem is solved through a particular implementation of a direct pseudo-spectral method for which initial guesses are generated through a relatively simple and straightforward genetic algorithm search on the optimal launch date and sail attitude. The results show that the trajectories take 2.16–4.21 years to complete, depending on the assumed solar-sail reflectance model and solar-sail technology. To assess the performance of solar-sail propulsion for this mission, the trajectory is also designed assuming the use of solar electric propulsion. The resulting fuel-optimal trajectories take longer to complete than the solar-sail trajectories and require a propellant consumption that exceeds the expected propellant capacity onboard the CubeSat. This comparison demonstrates the superior performance of solar-sail technology for this mission.