  We propose in this paper a scenario of spontaneous baryogenesis in
cosmological models of Quintessence by introducing a derivative coupling of the
Quintessence scalar $Q$ to the baryon current $J_B^{\mu}$ or the current of the
baryon number minus lepton number $J_{B-L}^{\mu}$. We find that with a
dimension-5 operator ${\partial_\mu Q} J_{B-L}^{\mu}$ suppressed by the Planck
mass $M_{pl}$ or the Grand Unification Scale $M_{GUT}$, baryon number asymmetry
$n_B/s \sim 10^{-10}$ can be naturally explained {\it via} leptogenesis. We
study also the isocurvature baryon number fluctuation generated in our model.
