This paper investigates the Cauchy problem for the full compressible Navier–Stokes–Korteweg equations, which model fluid dynamics with capillary properties in ${\mathbb{R}}^d(d\ge 3)$. And the global well-posedness and Gevrey analytic of strong solutions for the system are established in the $L^2-L^p$ type critical hybrid Besov space with $2\le p\le \frac{2d}{d-2}$ and $p<d$.