A numerical algorithm is proposed in this paper to solve a class of continuous-time linear fractional programming problems (CLFP). We shall transform (CLFP) into a continuous-time nonlinear programming problem. In order to tackle this nonlinear problem, we propose the auxiliary problem that will be formulated as parametric continuous-time linear programming problem. Following our recent works for solving continuous-time linear programming problems, we also introduce the discrete approximation method to solve the auxiliary problem. By using the solutions of the auxiliary problems, we can find the approximate solutions of (CLFP) and establish the estimation of error bound. Finally, we provide a numerical example to demonstrate the usefulness of this practical algorithm.