Reducing the number of individuals involved in substance abuse in any community is usually a challenging problem. We consider the control of the spread of Marijuana smoking, one substance that is majorly abused, among adults. We propose a deterministic model for controlling the spread of Marijuana smoking incorporating education and awareness campaign as well as rehabilitation as control measures. We formulate a ixed time optimal control problem subject to the model dynamics with the goal of inding the optimal combination of the control measures that will minimize the cost of the control efforts as well as the prevalence of marijuana smoking in a community. We use Pontryagin's maximum principle to derive the optimality system and solve the system numerically. Results from our simulations are discussed.