  In this paper, we study the Bergman kernel $B_\varphi(x,y)$ of generalized
Bargmann-Fock spaces in the setting of Clifford algebra. The versions of
$L^2$-estimate method and weighted subharmonic inequality for Clifford algebra
are established. Consequently we show the existence of $B_\varphi(x,y)$ and
then give some estimates on and off the diagonal. As a by-product, we also
obtain an upper estimate of the weighted harmonic Bergman kernel.
