The paper presents an on-demand routing algorithm that has the capability of maximizing the lifetime of a wireless ad hoc network. A key concept is in the time delay route request sent by each node, with a given delay that is inversely proportional to the residual battery capacity of the node. With this concept, routes are fully distributively constructed, while power consumption among nodes is balanced. To validate its performance, we have compared our algorithm with recently proposed ones (see Toh, C.-K. et al., Proc. IEEE ICC, p.2824-9, 2001).