Abstract: When establishing a mathematical model for steady-state operation of natural gas pipeline network, it is necessary to introduce 0-1 integer variables to describe the compressor's combination mode, thereby increasing the solving difficulty. To solve this problem, the compressor head characteristic curve is smoothly extended to the interval between the maximum compressor speed and zero, and the optimization of the mathematical model for steady-state operation of natural gas pipeline network is converted from mixed-integer nonlinear optimization to continuous nonlinear optimization by means of the function extension based on the continuous derivation of spline function. It is shown that the integer variables of optimization model can be removed effectively by extending the compressor characteristics curve while the physical significance of the compressor combination mode is not influenced. Obviously, it provides a way to reduce the solving difficulty of the mathematical model for steady-state operation optimization of natural gas pipeline network.