Gas-fired power plants are environmentally friendly because of their high efficiency rates and low CO2 emissions. On the other hand, the output power of renewable generators is stochastic, meaning that additional capacity must be held in reserve throughout the system. Gas-fired power plants are ideally suited to mitigate renewable uncertainties as they are more flexible and can easily be fired up in just a few minutes, and subsequently be shut down. Increased use of gas-fired power plants makes gas and electricity networks more dependent, so that adequacy in fuel supply of electricity network becomes a majority. However expansion planning of gas and electricity systems is accomplished by private gas and electricity companies, having no effective data exchange mechanism together. So there is a need to provide a model that coordinates the expansion planning of gas and electricity networks. On the other hand, expansion cost of either gas or electricity network and risk criteria of integrated energy system may have priority in decision-making process. With different challenging attributes, there is a gap in the literature to provide a model that takes into account the privacy of energy parties with a minimum data exchange, while considering different attributes in decision-making process. In this paper a multi-attribute decision-making (MADM) method for co-expansion planning of gas and electricity systems is introduced. The proposed MADM method supposes that a central entity as Ministry of Energy (ME) is responsible for coordinated expansion planning of gas and electricity networks, while taking into account the privacy of gas and electricity energy parties. Decision-making attributes are conflicting and the proposed method selects the best plan based on a compromise among the attributes. Different attributes including gas expansion cost (GEC), electricity expansion cost (EEC), minimum of maximum regret (MMR) and β-robustness (β_R) are considered to find the best plan with regard to the preferences of independent gas and electricity network operators. In this regard, two multi-attribute decision analysis methodologies are employed: analytical hierarchy process (AHP) is used as a simple way to weight and rank all the attributes objectively and find the relative importance of various plans, and the weighted sum method to provide a general composite index and finding the final appropriate plan. A real case study in the Khorasan province of Iran, which has a high penetration level of gas-consuming generation units (GCGU), is utilized to demonstrate the effectiveness of proposed MADM method. Results are compared with a Pareto optimal method to qualify the accuracy of proposed method.