We find evidence that the mass MBH of central supermassive black holes (SMBHs) correlates with the velocity dispersion sigma_GC of globular cluster systems of their host galaxies. This extends the well-known MBH - sigma_sph relation between black hole mass and velocity dispersion of the host spheroidal component. We compile published measurements of both MBH and sigma_GC for a sample of 13 systems and find the relation log(MBH) = alpha + beta log(sigma_GC/200) with alpha = 8.63 \pm 0.09 and

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... = 3.76 \pm 0.52. We also consider blue (metal-poor) and red (metal-rich) globular clusters sub-populations separately and obtain a surprisingly tight correlation using only the velocity dispersion sigma_GC^red of the red clusters with alpha = 8.73 \pm 0.09 and beta = 3.84 \pm 0.52 and an intrinsic scatter eps_0 = 0.22 dex compared to eps_0 = 0.27 dex for the MBH - sigma_sph of our sample. We use our MBH - sigma_GC relation to estimate the central black hole mass in five galaxies for which sigma_GC^red is measured.