  For the Klein group $K$ and a positive integr $k$, irreducible modules of the
orbifold vertex operator algebra $L_{\widehat{\mathfrak{sl}_2}}(k,0)^{K}$ have
been classified and constructed in \cite{JWa}. In this paper, we determine
completely the fusion rules of $L_{\widehat{\frak{sl}_2}}(k,0)^{K}$.
