  The admissible modules for $\hat{sl}_2$ are studied from the point of view of
vertex operator algebra. If $l$ is rational such that $l+2={p\over q}$ for some
coprime positive integers $p\ge 2$ and $q$, Kac and Wakimoto found finitely
many distinguished irreducible representations for $\hat{sl}_2$, called
admissible representations. In this paper we prove that the vertex operator
algebra $L(l,0)$ associated to irreducible highest weight representation of $l$
is not rational if $l$ is not a positive integer. However if we change the
Virasoro algebra in certain way, $L(l,0)$ becomes a rational vertex operator
algebra whose irreducible representations are exactly those admissible
representations. We show that the $q$-dimensions with respect to the new
Virasoro algebra are modular functions. We aslo calculate the fusions rules.
