Lack of national budgets, high capital cost of infrastructure projects in power transmission grid and associated risks are among serious complications for transmission system expansion. A fundamental solution to overcoming these difficulties is attracting private sector capital to finance these projects. However private sector participation requires a certain level of profitability and risk management. In this paper a framework for attracting merchant investment to finance power projects has been proposed which can be adapted in other energy infrastructure systems. In the proposed algorithm, maximizing merchant investment is formulated as an objective function in the process of transmission expansion planning problem .The objective functions and constraints such as minimizing the construction cost of transmission lines, minimizing congestion costs, maximizing absorbed private investment and investment risks are used for problem modeling. The scenario analysis is used for modeling uncertainties; the NSGA II algorithm is used to obtain pareto-optimal solutions and the fuzzy satisfying method is used to choose the best solution. Final results are shown on the IEEE 24Bus reliability test system. With the proposed method the system planner can be assured about maximized merchant investment and also the profitability and risk hedging could be guaranteed for private sector investors.