Molybdenum, as an important structural material, has been widely used in nuclear energy systems. Therefore, the high-precision neutron reaction cross-section of molybdenum is of great significance for developing nuclear energy systems. This paper uses activation and relative measurement methods to measure the reaction cross section of ⁹²Mo(n,p)^92mNb. The sample is irradiated at a 90º angle using nanosecond pulse neutron generator (CPNG) from the China Institute of Atomic Energy. After a period of cooling time, the activities of the activated product nuclei of the irradiated sample are measured using a high-purity germanium detector, and the reaction cross section and correction factors are calculated. The traditional correction factors include neutron fluence fluctuation, cascade, self-absorption, geometry and scattered-neutron corrections. Finally, the reaction cross section of ⁹²Mo(n,p)^92mNb at 14.1-MeV energy point is obtained. In order to reduce the uncertainty of experimental measurements, this work proposes a strategy in which the test product and the monitoring product are the same nuclide, effectively eliminating the uncertainties caused by the half-life and decay branch ratio of the product nucleus, gamma detection efficiency, and beam fluctuations during irradiation. This method significantly enhances the measurement accuracy, achieving the highest precision experimental data to date. This experiment aims to minimize the overall measurement uncertainty, so the stringent requirements are imposed on both the sample mass-thickness and the operating environment. The mass and thickness of each sample are therefore determined through five independent measurements using a 0.1 mg-precision analytical balance and a vernier caliper, respectively, and the mean values are taken. After the experiment, the measured data are carefully compared and analyzed with other datasets, The value of cross-section is not significantly different from others in the database and is located within the error range, which further verifies the feasibility of this method, providing high-precision experimental support for evaluating the nuclear-data of this reaction channel.