Previous studies of optimal trading strategies have neglected the exogenous institutional constraints of trading speeds. Under the weak-form efficient market hypothesis,this paper builds an investment utility maximization model for trading strategies in the presence of limits on trading speeds. Applying the maximum principle,the closed-form solutions of optimal trading strategies under different market conditions and various initial positions are derived. A further analysis of optimal trading strategies indicates that there exists an optimal initial position( i. e. opportunity capacity) which maximizes the investor's utility. Also,the investor needs to trade at the maximum speed to adjust the position with the opportunity capacity as the target at the initial stage of the investment horizon,and to liquidate the position at the final stage.