Monthly-mean data of ERA-Interim reanalysis, precipitation, outgoing longwave radiation (OLR) and sea surface temperature(SST) are investigated for 40 years (1979-2018) to reveal the modulation of the global monsoon systems by the equatorial quasi-biennial oscillation (QBO), focusing only on the neutral El Niño-Southern Oscillation (ENSO) periods (in total 374 months). First, the climatology of the global monsoon systems is viewed with longitude-latitude plots of the precipitation, its proxies and lower tropospheric circulations for the annual mean and two solstice seasons, together with the composite differences between the two seasons. In addition to seasonal variations of Intertropical Convergence Zones (ITCZs), several regional monsoon systems are well identified with an anti-phase of the annual cycle between the two hemispheres. Precipitation-related quantities (OLR and specific humidity), surface conditions [i.e., mean sea level pressure (MSLP) and SST] and circulation fields related to moist convection systems show fundamental features of the global monsoon systems. After introducing eight QBO phases based on the leading two principal components of the zonal-mean zonal wind variations in the equatorial lower-stratosphere, the statistical significance of the composite difference in the precipitation and tropospheric circulation is evaluated for the opposite QBO phases. The composite differences show significant modulations in some regional monsoon systems, dominated by zonally asymmetric components, with the largest magnitudes for specific QBO-phases corresponding to traditional indices of the equatorial zonal-mean zonal wind at 20 and 50 hPa. Along the equator, significant QBO influence is characterized by the modulation of the Walker circulation over the western Pacific. In middle latitudes during boreal summer, for a specific QBO-phase, statistically significant modulation of low-pressure cyclonic perturbation is obtained over the Northern-Hemisphere western Pacific Ocean associated with statistically significant features of heavier precipitation over the eastern side of the cyclonic perturbation and the opposite lighter precipitation over the western side. During boreal winter, similar significant low-pressure cyclonic perturbations were found over the Northern-Hemisphere eastern Pacific and Atlantic Oceans for specific phases.