  In this paper, we study the existence of normalized solutions to the
following nonlinear Schr\"{o}dinger equation \begin{equation*} \left\{
\begin{aligned} &-\Delta u=f(u)+ \lambda u\quad \mbox{in}\ \mathbb{R}^{N},\\
&u\in H^1(\mathbb{R}^N), ~~~\int_{\mathbb{R}^N}|u|^2dx=c, \end{aligned} \right.
\end{equation*} where $N\ge3$, $c>0$, $\lambda\in \mathbb{R}$ and $f$ has a
Sobolev critical growth at infinity but does not satisfies the
Ambrosetti-Rabinowitz condition. By analysing the monotonicity of the ground
state energy with respect to $c$, we develop a constrained minimization
approach to establish the existence of normalized ground state solutions for
all $c>0$.
