Optimum solution of time-cost trade-off problem has significant importance since it provides the highest profit opportunity. For this reason, exact, heuristic, and meta-heuristic algorithms are adapted to obtain the optimum or near-optimum solution. However, heuristic algorithms may not always converge into the global optimum, while meta-heuristic algorithms require significant computation to converge into global optimum and exact methods are complex for construction planners to implement. Therefore, minimum cost-slope based fast converging network analysis algorithm, which provides optimum or near-optimum solutions, is proposed for discrete time-cost trade-off problem. The algorithm searches the global optimum through the feasible crashing options. Number of feasible crashing options increase tremendously in large projects. Therefore, an elimination algorithm is embedded to reduce the number of crashing options. The crashing option with the lowest unit crashing cost is executed and global optimum is searched by stepwise crashing. Tests on 18 and 63-Activity projects revealed that the network analysis algorithm converges to optimum or near-optimum solution by only one percent of the computational demand of meta-heuristic algorithms. Consequently, the proposed heuristic algorithm is a convenient optimization method for the solution of time-cost trade-off problem.