Quasi-periodic fast-propagating ( QFP ) magnetosonic waves and extreme ultraviolet ( EUV ) waves were proposed to be driven by solar flares and coronal mass ejections ( CMEs ) , respectively . In this Letter , we present a detailed analysis of an interesting event in which we find that both QFP magnetosonic waves and EUV waves are excited simultaneously in one solar eruption event . The co-existence of the two wave phenomena offers an excellent opportunity to explore their driving mechanisms . The QFP waves propagate in a funnel-like loop system with a speed of 682–837 km s ^ { -1 } and a lifetime of 2 minutes . On the contrary , the EUV waves , which present a faster component and a slower component , propagate in a wide angular extent , experiencing reflection and refraction across a magnetic quasi-separatrix layer . The faster component of the EUV waves travels with a speed of 412–1287 km s ^ { -1 } , whereas the slower component travels with a speed of 246–390 km s ^ { -1 } . The lifetime of the EUV waves is \sim 15 minutes . It is revealed that the faster component of the EUV waves is cospatial with the first wavefront of the QFP wave train . Besides , The QFP waves have a period of about 45 \pm 5 seconds , which is absent in the associated flares . All these results imply that QFP waves can also be excited by mass ejections , including CMEs or jets .