With more accurate measurement method for gas samples, cross sections of the 14N(n,α0,1)11B reactions were measured at 24 energy points in the 4.5–11.5 MeV neutron energy region based on the 4.5 MV Van de Graaff accelerator at Peking University and the HI-13 tandem accelerator of China Institute of Atomic Energy (CIAE). The average neutron fluence (Φ) through the gas sample was obtained through the combination of a highly enriched 238U3O8 sample and the simulation based on SuperMC. The cross sections of the 14N(n,α0)11B reaction measured using the gas sample and the solid samples are in agreement with each other. R-matrix analysis was carried out for the n + 14N system using code RAC in the neutron energy region below 30 MeV. A possible valley structure in both the excitation functions of the 14N(n,α0,1)11B reactions in the 10–11 MeV neutron energy region was found for the first time.