The pipe roughness coefficient is a crucial parameter in oil field water injection networks, directly affecting the accuracy of hydraulic calculations and operational optimization. This paper proposed a mathematical model to calibrate the pipe roughness coefficient under a single operating condition, using matrix singular value decomposition to convert the problem into a positive definite quadratic programming model. The interior-point method was employed to solve this problem, yielding a global optimal solution. Simulation results on an actual network showed that the proposed method reduced the average error of the roughness coefficient by 4.9%, from 7.08% to 2.18%, demonstrating its effectiveness.