A convex network problem is a mathematical program where the objective function is convex and the constraint set is a network with flow conservation at each node. Further there are upper and lower bounds associated with each edge. In this paper, we construct the dual of such a program and hence reduce the dimension of the problem from that of the arc set of the underlying network to that of the node set. Further the dual program is unconstrained. Generally this reduction is significant and in one particular case, the dimension is reduced to unity and hence trivially solvable. The mathematical machinery is provided by the duality theory of generalized geometric programming.