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In this paper, we continue to construct stationary classical solutions of theincompressible Euler equation approximating singular stationary solutions ofthis equation.  This procedure now is carried out by constructing solutions to the followingelliptic problem \[  {cases} -\ep^2 \Deltau=(u-q-\frac{\kappa}{2\pi}\ln\frac{1}{\ep})_+^p-(q-\frac{\kappa}{2\pi}\ln\frac{1}{\ep}-u)_+^p,\quad & x\in\Omega, u=0, \quad & x\in\partial\Omega, {cases} \] where $p>1$,$\Omega\subset\mathbb{R}^2$ is a bounded domain, $q$ is a harmonic function.  We showed that if $\Omega$ is a simply-connected smooth domain, then for anygiven non-degenerate critical point of Kirchhoff-Routh function$\mathcal{W}(x_1^+,...,x_m^+,x_1^-,...,x_n^-)$ with$\kappa^+_i=\kappa>0\,(i=1,...,m)$ and $\kappa^-_j=-\kappa\,(j=1,...,n)$, thereis a stationary classical solution approximating stationary $m+n$ points vortexsolution of incompressible Euler equations with total vorticity $(m-n)\kappa$.

Regularization of point vortices for the Euler equation in dimension two, part II