The frictional resistance coefficient of ventilation of a roadway in a coal mine is a very important technical parameter in the design and renovation of mine ventilation. Calculations based on empirical formulae and field tests to calculate the resistance coefficient have limitations. An inversion method to calculate the mine ventilation resistance coefficient by using a few representative data of air flows and node pressures is proposed in this study. The mathematical model of the inversion method is developed based on the principle of least squares. The measured pressure and the calculated pressure deviation along with the measured flow and the calculated flow deviation are considered while defining the objective function, which also includes the node pressure, the air flow, and the ventilation resistance coefficient range constraints. The ventilation resistance coefficient inversion problem was converted to a nonlinear optimisation problem through the development of the model. A genetic algorithm (GA) was adopted to solve the ventilation resistance coefficient inversion problem. The GA was improved to enhance the global and the local search abilities of the algorithm for the ventilation resistance coefficient inversion problem.