The cross power spectrum of the 21 cm signal and Lyman-α emitters (LAEs) is a probe of the Epoch of Reionization. Astrophysical foregrounds do not correlate with the LAE distribution, though the foregrounds contribute to the error. To study the impact of foregrounds on the measurement, we assume realistic observation by the Murchison Widefield Array using a catalogue of radio galaxies, a LAE survey by the Subaru Hyper Supreme-Cam and the redshift of LAEs is determined by the Prime Focus Spectrograph. The HI distribution is estimated from a radiative transfer simulation with models based on results of radiation hydrodynamics simulation. Using these models, we found that the error of cross power spectrum is dominated by foreground terms. Furthermore, we estimate the effects of foreground removal, and find 99% of the foreground removal is required to detect the 21 cm-LAE signal at k ∼ 0.4 h Mpc−1.