This work studies the Paschen law in electrical breakdown of a mixed geometry disc - conical electrodes from aluminum material at constant 10 cm distance using nitrogen gas. The discharge characteristices including discharge voltage, discharge current and breakdown voltage against the pressure-distance multiplied were measured at different pressures. The secondary electron emission coefficient was calculated using Townsend's secondary ionization coefficient equation. A comparison between two similar disc and conical structures with a mixed disc - conical structure was made for the breakdown voltage, discharge current and secondary electron emission coefficient. It is concluded that the values of secondary electron emission coefficient of conical cathode are higher than of disc cathode due to higher ions density on conical cathode than that disc one.