We demonstrated AlGaN multi-quantum well (MQW) deep ultraviolet (UV) light-emitting diodes (LEDs) with wavelength in the range of 227-261 nm fabricated on high-quality AlN buffers on sapphire substrates. We achieved crack-free, thick AlN buffer on sapphire with low threading dislocation density (TDD) and atomically flat surface by introducing an ammonia (NH_3) pulse-flow multi-layer (ML) growth method through metal-organic chemical vapor deposition (MOCVD). The edge- and screw-type dislocation densities of AlGaN layer on AlN buffer were reduced to 7.5×10^8 and 3.8×10^7 cm^<-2>, respectively, by using a ML-AlN buffer. We achieved single-peaked high-brightness operations of AlGaN deep-UV LEDs by fabricating them on the ML-AlN buffers on sapphire substrates. The maximum output power and external quantum efficiency (EQE) of the 261 nm and 227.5 nm LEDs were 1.65 mW and 0.23% under room-temperature (RT) CW operation, and 0.15 mW and 0.2%, under RT pulsed operation, respectively.