We discuss the prospects for directly detecting a circular polarization signal of the gravitational-wave background. We find it is generally difficult to probe the monopole mode of the signal due to the broad directivity of the gravitational-wave detectors. But the dipole (l=1) and octupole (l=3) modes of the signal can be measured in a simple manner by combining outputs of two unaligned detectors, and we can dig them deeply under confusion and detector noises. Around f similar to 0.1 mHz the Laser Interferometer Space Antenna will provide ideal data streams to detect these patterns whose magnitudes are as small as similar to 1 percent of the detector noise level in terms of the nondimensional energy density Omega(GW)(f).