  We investigate the big-bang nucleosynthesis in a Brans-Dicke model with a
varying $\Lambda$ term using the Monte-Carlo method and likelihood analysis. It
is found that the cosmic expansion rate differs appreciably from that of the
standard model. The produced abundances of $^4$He, D, and barely Li are
consistent with the observed ones within the uncertainties in nuclear reaction
rates when the baryon to photon ratio $\eta = (5.47 - 6.64)\times 10^{-10}$,
which is in agreement with the value deduced from WMAP.
