Arrival-time spectra (ATS) of an electron swarm in N2 from 50 Td to 700 Td (1 Td = 10−17 Vcm2) were measured by double-shutter drift tube, and then the first Townsend ionization coefficient, mean-arrival-time drift velocity, longitudinal diffusion coefficient, and longitudinal third-order transport coefficient were obtained from the measured ATS. This is the first successful measurement of the third-order transport coefficient in a gas. Furthermore, we went back to an expression of the longitudinal diffusion coefficient in terms of the α parameter, which is the electron transport coefficient derived from ATS, and then demonstrated that the third-order and higher-order electron transport coefficients, which are traditionally ignored in the electron swarm experiment, should be considered to obtain the longitudinal diffusion coefficient properly at moderate and high reduced electric fields.