Crystallinity of an 80-nm-thick bismuth thin film grown on Si(111) substrate by MBE was investigated. The highly (0003) textured Bi film contains two twinning domains with different bilayer stacking sequences. The basic lattice parameters c and a as well as b, the bilayer thickness, of the two domains were determined from a series of X-ray diffraction (XRD) measurements, and found that the differences are within 0.1% as compared with those of bulk Bi reported in literature, suggesting that the Bi film has been nearly fully relaxed. From the XRD φ-scans of asymmetric Bi (01-14), (10-15), (11-26) planes and Si (220) plane as well as selected area electron diffraction patterns and electron back scatter diffraction pole figures, we confirmed the well registration between the lattices of Si and Bi lattice, i.e. the ω angle difference between Bi[0003] and Si[111] and the φ angle different between Bi[01-14] and Si[220] are 0.056° and 0.25°, respectively, and thus concluded that the growth is a quasi-van der Waals epitaxy.