String-topology multi-hop network is often selected as an analysis object because it is one of the fundamental network topologies. The purpose of this paper is to establish expression for end-to-end delay for IEEE 802.11 string-topology multi-hop networks. For obtaining the analytical expression, the effects of frame collisions and carrier-sensing effect from other nodes under the non-saturated condition are obtained for each node in the network. For expressing the properties in non-saturated condition, a new parameter, which is frame-existence probability, is defined. The end-to-end delay of a string-topology multi-hop network can be derived as the sum of the transmission delays in the network flow. The analytical predictions agree with simulation results well, which show validity of the obtained analytical expressions.