The detection of gravitational waves (GWs) provides a direct way to measure the luminosity distance, which enables us to probe cosmology. In this paper, we continue to expand the application of GW standard sirens in cosmology, and propose that the spatial curvature can be estimated in a model-independent way by comparing the distances from future GW sources and current cosmic-chronometer observations. We expect an electromagnetic counterpart of the GW event to give the source redshift, and simulate hundreds of GW data from the coalescence of double neutron stars and black hole-neutron star binaries using the Einstein Telescope as a reference. Our simulations show that, fr(o)m 100 simulated GW events and 31 current cosmic-chronometer measurements, the error of the curvature parameter Omega(K) is expected to be constrained at the level of similar to 0.125. If 1000 GW events were observed, the uncertainty of Omega(K) would be further reduced to similar to 0.040. We also find that adding 50 mock H(z) data points (consisting of 81 cosmic-chronometer data points and 1000 simulated GW events) could result in a much tighter constraint on the zero cosmic curvature, for which Omega(K) = -0.002 +/- 0.028. Compared to some actual model-independent curvature tests involving distances from other cosmic probes, this method using GW data achieves constraints with much higher precision.