This paper examines the impact of speed limits on network efficiency, in terms of total travel time of all road users, and equity among road users from different origin-destination (OD) pairs, in terms of the change of travel time after imposing a speed limit scheme. We find that after imposing a speed limit scheme, the total travel time of all road users may decrease or increase; road users of some OD pairs may experience longer travel time, while other OD pairs may have shorter travel time. In view of the importance of speed limits on network efficiency and equity, we subsequently develop a bi-level programming model for designing the optimal speed limit scheme that maximizes the network efficiency while considering the equity issue. A global optimization approach that is suitable for bilevel programming models with finite discrete upper-level decision variables is proposed. Moreover, a conic quadratic mixed-integer linear programming approach is developed to solve relaxed models of the bi-level formulation of speed limit design. Two numerical examples are carried out.