We find evidence that the mass MBH of central supermassive black holes (SMBHs) correlates with the velocity dispersion σGC of globular cluster systems of their host galaxies. This extends the well-known MBH–σsph relation between black hole mass and velocity dispersion of the host spheroidal component. We compile published measurements of both MBH and σGC for a sample of 13 systems and find the relation log (MBH) =α+βlog (σGC/200), with α= 8.63 ± 0.09 and β= 3.76 ± 0.52. We also consider blue (metal-poor) and red (metal-rich) globular cluster subpopulations separately and obtain a surprisingly tight correlation using only the velocity dispersion of the red clusters with α= 8.73 ± 0.09 and β= 3.84 ± 0.52 and an intrinsic scatter ɛ0= 0.22 dex compared to ɛ0= 0.27 dex for the MBH–σsph relation of our sample. We use this MBH– relation to estimate the central black hole mass in five galaxies for which is measured.