It was observed that an electron energy distribution function (EEDF) in a nitrogen afterglow plasma has two Maxwellian distributions in a thermal region and a vibrational excitation region with temperatures of T_c and T_v (equal to the vibrational temperature of molecules), and that the magnitude of T_v is greater than that of the stationary state of T_e. A new method is proposed for the determination of the molecules vibrational temperature by measuring the EEDF in the afterglow plasma. The magnitude T_c does not vary significantly and is determined by the heating and cooling balance between the thermal electrons and fast elections. These fast electrons arise from superdastic collisions of the thermal electrons with vibrationally excited molecules. The measurements of the EEDF were made at 100 μs intervals during the relaxation period which lasted about 500 μs after the discharge.