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In this paper, we are concerned with the following type of fractionalproblems:  $$  \begin{cases}\dis  (-\Delta)^{s} u-\mu\frac{u}{|x|^{2s}}-\lambda u=|u|^{2^*_{s}-2}u+f(x,u),&\text{in} \Omega,\ \  \,  u=0\,&\text{in} \R^N\backslash\Omega  \end{cases}  \eqno {(*)} $$  where $s\in (0,1)$, $2^*_{s}=2N/(N-2s)$ is the critical Sobolev exponent,$f(x,u)$ is a lower order perturbation of critical Sobolev nonlinearity. Weobtain the existence of the solution for (*) through variational methods. Inparticular we derive a Br\'ezis-Nirenberg type result when $f(x,u)=0$.

The Brezis-Nirenberg Result for the Fractional Elliptic Problem with Singular Potential