In this paper we consider a class of infinite-dimensional linear programming problems, called continuous-time linear programming problems (CLP). In our previous paper, we presented a discrete approximation method for solving (CLP) and established the estimation for error bounds of searched numerical solutions. However, the computation times involved can be very large as a result of solving a very large finite-dimensional linear program. We will focus on a special class of (CLP) and provide improved methods to overcome the computational bottleneck.