A bilinear dynamical system can be used to represent the model of a network in which the state obeys linear dynamics and the input is the edge weight of certain controlled edges in the network. We present algebraic and graph-theoretic conditions for the structural controllability of a class of bilinear systems with a single control where the input matrix is rank one. Subsequently, we use these conditions, given a system state graph, to develop an algorithm to design the location of controlled edges (the input matrix) such that the system is structurally controllable. (C) 2015 Elsevier Ltd. All rights reserved.