  The centre of two-parameter quantum groups $U_{r,s}(\mathfrak{g})$ is
determined through the Harish-Chandra homomorphism. Based on the Rosso form and
the representation theory of weight modules, we prove that when rank
$\mathfrak{g}$ is even, the Harish-Chandra homomorphism is an isomorphism, and
in particular, the centre of the quantum group $\breve{U}_{r,s}(\mathfrak{g})$
of the weight lattice type is a polynomial algebra
$\mathbb{K}[z_{\varpi_1},\cdots,z_{\varpi_n}]$, where canonical central
elements $z_\lambda \; (\lambda \in \Lambda^+)$ are turned out to be uniformly
expressed. For rank $\mathfrak{g}$ to be odd, we figure out a new invertible
extra central generator $z_*$, which doesn't survive in $U_q(\mathfrak g)$, and
we get a larger centre containing
$\mathbb{K}[z_{\varpi_1},\cdots,z_{\varpi_n}]\otimes_\mathbb K\mathbb K[z_*,
z_*^{-1}]$.
