  The synthesis of helium in the early Universe depends on many input
parameters, including the value of the gravitational coupling during the period
when the nucleosynthesis takes place. We compute the primordial abundance of
helium as function of the gravitational coupling, using a semi-analytical
method, in order to track the influence of $G$ in the primordial
nucleosynthesis. To be specific, we construct a cosmological model with varying
$G$, using the Brans-Dicke theory. The greater the value of $G$ at
nucleosynthesis period, the greater the abundance of helium predicted. Using
the observational data for the abundance of the primordial helium, constraints
for the time variation of $G$ are established.
