  For a positive braid link, a link represented as a closed positive braids, we
determine the first few coefficients of its HOMFLY polynomial in terms of
geometric invariants such as, the maximum euler characteristics, the number of
split factors, and the number of prime factors. Our results give improvements
of known results for Conway and Jones polynomial of positive braid links. In
Appendix, we present a simpler proof of theorem of Cromwell, a positive braid
diagram represent composite link if and only if the the diagram is composite.
