It takes some time for taxi driver to complete a requested service of passengers and the driver can attend to only one service at a time, and this distinguishes taxi service from ordinary goods. This paper deals with an incremental discount policy on the taxi fare. It is assumed that customers arrive following a Poisson process with price-sensitive arrival rates. With the objective of maximizing the average profit of taxi, a mathematical model is developed based on regenerative process. Through an analysis of the model, we show that the incremental discount policy is beneficial to the taxi company when the customer arrival rate is relatively small. Also, we propose a solution procedure to determine the optimal discount rate and price breakpoint. Finally, test problems are solved for sensitivity studies. (C) 2007 Elsevier B.V. All rights reserved.