  We describe a finite presentation of $ \mathcal{T}_{g,r} $ for $g \geq 3$. %
or $(g,r)=(2,0)$. Here $\mathcal{T}_{g,r} $ is the universal central extension
of the mapping class group of the surface of genus $g$ with $r$-boundaries. We
also investigate the case $g=2$,
