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In this paper, we consider the existence and multiplicity of normalizedsolutions for the following $p$-Laplacian critical equation  \begin{align*}  \left\{\begin{array}{ll}  -\Delta_{p}u=\lambda\lvert u\rvert^{p-2}u+\mu\lvert u\rvert^{q-2}u+\lvertu\rvert^{p^*-1}u&\mbox{in}\ \mathbb{R}^N,  \int_{\mathbb{R}^N}\lvert u\rvert^pdx=a^p,  \end{array}\right.  \end{align*} where $1<p<N$, $2<q<p^*=\frac{Np}{N-p}$, $a>0$,$\mu\in\mathbb{R}$ and $\lambda\in\mathbb{R}$ is a Lagrange multiplier. Usingconcentration compactness lemma, Schwarz rearrangement, Ekeland variationalprinciple and mini-max theorems, we obtain several existence results under$\mu>0$ and other assumptions. We also analyze the asymptotic behavior of theresolutions as $\mu\rightarrow 0$ and $\mu$ goes to its upper bound. Moreover, weshow the nonexistence result for $\mu<0$ and get that the $p$-Laplacianequation has infinitely solutions by genus theory when $p<q<p+\frac{p^2}{N}$.

Normalized solutions for $p$-Laplacian equation with critical Sobolev exponent and mixed nonlinearities