  In this paper, we study the motion of the two dimensional inviscid
incompressible, infinite depth water waves with point vortices in the fluid. We
show that Taylor sign condition $-\frac{\partial P}{\partial \boldmath{n}}\geq
0$ can fail if the point vortices are sufficient close to the free boundary, so
the water waves could be subject to the Taylor instability. Assuming the Taylor
sign condition, we prove that the water wave system is locally wellposed in
Sobolev spaces. Moreover, we show that if the water waves is symmetric with a
certain symmetric vortex pair traveling downward initially, then the free
interface remains smooth for a long time, and for initial data of size
$\epsilon\ll 1$, the lifespan is at least $O(\epsilon^{-2})$.
