The growth of semi-polar (112[combining macron]2) GaN/InGaN multiple-quantum-well (MQW) co-axial heterostructure shells around m-axial GaN core nanowires on a Si substrate using MOCVD is reported for the first time. The core GaN nanowire and GaN/InGaN MQW shells are grown in a two-step growth sequence of vapor-liquid-solid and vapor-solid growth modes. The luminescence and carrier dynamics of GaN/InGaN MQW coaxial nanowires are studied by photoluminescence, cathodoluminescence, and low temperature time-resolved photoluminescence (TRPL). The emission is tuned from 430 nm to 590 nm by increasing the InGaN QW thickness. The non-single exponential decay measured by low-temperature TRPL was attributed to the indium fluctuations in the InGaN QW. The ultrafast radiative lifetime was measured from 14 ps to 26 ps with different emission wavelengths at a very high internal quantum efficiency up to 68%. An ultrafast carrier lifetime was assigned to the growth of the InGaN QW on semi-polar (112[combining macron]2) growth facet and the improved carrier collection efficiency due to the radial growth of the GaN/InGaN MQW shells. Such an ultrafast carrier dynamics of NWs provides a meaningful active medium for high speed optoelectronic applications.