  We report on detailed spectroscopic studies performed for the secondary star
in the black hole binary (micro-quasar) V4641 Sgr in order to examine its
surface chemical composition and to see if its surface shows any signature of
pollution by ejecta from a supernova explosion. High-resolution spectra of
V4641 Sgr observed in the quiescent state in the blue-visual region are
compared with those of the two bright well-studied B9 stars (14 Cyg and $\nu$
Cap) observed with the same instrument. The effective temperature of V4641 Sgr
(10500 $\pm$ 200 K) is estimated from the strengths of He~{\sc i} lines, while
its rotational velocity, $\it v$ sin $\it i$ (95 $\pm$ 10 km s${}^{-1}$), is
estimated from the profile of the Mg~{\sc ii} line at 4481 \AA. We obtain
abundances of 10 elements and find definite over-abundances of N (by 0.8 dex or
more) and Na (by 0.8 dex) in V4641 Sgr. From line-by-line comparisons of eight
other elements (C, O, Mg, Al, Si, Ti, Cr, and Fe) between V4641 Sgr and the two
reference stars, we conclude that there is no apparent difference in the
abundances of these elements between V4641 Sgr and the two normal late B-type
stars, which have been reported to have solar abundances. An evolutionary model
of a massive close binary system has been constructed to explain the abundances
observed in V4641 Sgr. The model suggests that the progenitor of the black hole
forming supernova was as massive as ~ 35 Msun on the main-sequence and, after
becoming a ~ 10 Msun He star, underwent "dark" explosion which ejected only N
and Na-rich outer layer of the He star without radioactive $^{56}$Ni.
