In this paper, we prove a $Tb$ theorem on product spaces $Bbb R^ntimes Bbb R^m$, where $b(x_1,x_2)=b_1(x_1)b_2(x_2)$, $b_1$ and $b_2$ are para-accretive functions on $Bbb R^n$ and $Bbb R^m$, respectively.