In a carbon-constrained world, the continuing and rapid growth of gas-fired power generation (GPG) will lead to the increasing demand for natural gas. The reliable and affordable gas supply hence becomes an important factor to consider in power system planning. Meanwhile, the installation of GPG units should take into account not only the fuel supply constraints but also the capability of sending out the generated power. In this paper, a novel expansion co-planning (ECP) model is proposed, aiming to minimize the overall capital and operational costs for the coupled gas and power systems. Moreover, linear formulations are introduced to deal with the nonlinear nature of the objective functions and constraints. Furthermore, the physical and economic interactions between the two systems are simulated by an iterative process. The proposed linear co-planning approach is tested on a simple six-bus power system with a seven-node gas system and a modified IEEE 118-bus system with a 14-node gas system. Numerical results have demonstrated that our co-planning approach can allow systematic investigations on supporting cost-effective operating and planning decisions for power systems.