Maser is an acronym for microwave amplification by stimulated emission of radiation; in astronomy mega-masers are masers in galaxies that are ≥ 10(6) times more luminous than typical galactic maser sources. Observational studies of mega-masers can help us to understand their origins and characteristics. More importantly, mega-masers can be used as diagnostic tracers to probe the physical properties of their parent galaxies. Since the late 1970s, only three types of molecules have been found to form mega-masers: H2O, OH and H2CO. Here we report the detection of both SiO and CH3OH mega-masers near the centre of Seyfert 2 galaxy NGC 1068 at millimetre wavelengths, obtained using the IRAM 30-m telescope. We argue that the SiO mega-maser originated from the nuclear disk and the CH3OH mega-maser originated from shock fronts. High-resolution observations in the future will enable us to investigate AGN feedback and determine the masses of central supermassive black holes in such galaxies.