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This study presents a novel approach for transmission expansion planning (TEP) addressing the inherent uncertainties associated with the estimated investment costs of candidate transmission lines and the forecasted electricity demands during long-term planning horizon. The proposed TEP approach employs a renovated mixed integer linear programming formulation holding the optimality and low computation burden of linear modelling techniques. The above mentioned uncertainties are encountered through robust optimisation methodology enabling the system's planner to assess different levels of uncertainty and conservation throughout planning horizon. The proposed robust TEP procedure is successfully applied to Garver 6-bus, IEEE 30-bus and IEEE 118-bus test systems. Simulation results demonstrate that the uncertainty level of investment costs and electricity demands escalates the total expansion costs based on the scale of power system.