Natural gas (NG) is widely transported through the high-pressure pipeline network. For maintaining the high pressure in the gas pipeline network, compressor stations are installed at fixed intervals along with the pipeline. The compression procedures involve huge amounts of energy and investment. So designing any pipeline network in NG transportation also needs to include conflicting goals of various criteria with the priority like maximization of demand satisfaction and minimization of compression energy and investment cost. In this paper, a goal programming approach dependent upon lexicographic methodology is proposed for solving the multi-criteria problem in NG transportation where each criterion is incorporated on a priority basis to achieve targeted goals. The relevance of the proposed model is explained via an example. Maximization in demand satisfaction is a prime objective and remaining targeted goals are attained on a priority basis. The deviation variable in the proposed model is solved in GAMS by using the CPLEX solver. These deviation variables provide flexibility to the decision-maker to change their priorities according to the social, environmental, and economical constraints.