In order to satisfy the growing travel demand and reduce the traffic congestion, the continuous network design problem (CNDP) is often proposed to optimize the road network performance by road capacity expansion. In determining the equilibrium travel flow pattern, equilibrium principles like deterministic user equilibrium (DUE) and stochastic user equilibrium (SUE) may be applied to describe the travelers’ routing choice behavior. Due to the different mathematical formulation structures for the CNDP with DUE and SUE, most of the existing solution algorithms have been developed to solve CNDP, either for DUE or SUE. In this study, we propose a more general solution method by applying the generalized geometric programming (GGP) approach to solve the global optimal solution of CNDP with both DUE and SUE. Specifically, the original CNDP problem is reformulated into a GGP form, then a successive monomial approximation method is employed to transform the GGP formulation into a standard geometric programming (GP) form, which can be cast into an equivalent nonlinear but convex optimization problem, whose global optimal solution can be guaranteed and solved by many existing solution algorithms. Numerical experiments are presented to demonstrate the validity and efficiency of the solution method.