  Primordial magnetic fields (PMFs) can source gravitational wave background
(GWB). In this paper, we investigate the possible constraints on small-scale
PMF considering the ongoing and forthcoming direct detection observations of
GWB. In contrast to the conventional cosmological probes, e.g., cosmic
microwave background anisotropies, which are useful to investigate large-scale
PMFs ($>1 {\rm Mpc}$), the direct detection experiments of GWB can explore
small-scale PMFs whose scales correspond to the observed frequencies of GWB. We
show that future ground-based or space-based interferometric gravitational wave
detectors give a strong constraint of about $10^{2} {\rm nG}$ on much smaller
scales of about $k\approx 10^{12} {\rm Mpc}^{-1}$. We also demonstrate that
pulsar timing arrays have a potential to strongly constrain PMFs. The current
limits on GWB from pulsar timing arrays can put the tight constraint on the
amplitude of the PMFs of about $30 {\rm nG}$ whose coherent length is of about
$k\approx 10^{6} {\rm Mpc}^{-1}$. The future experiments for the direct
detection of GWB by the Square Kilometre Array could give much tighter
constraints on the amplitude of PMFs about $5 {\rm nG}$ on $k\approx 10^{6}
{\rm Mpc}^{-1}$, on which scales, it is difficult to reach by using the
cosmological observations.
