AbstractThis paper concerns the lower bound decay rate of global solution for compressible Navier–Stokes–Korteweg system in three-dimensional whole space under the$$H^{4}\times H^{3}$$H4×H3framework. At first, the lower bound of decay rate for the global solution converging to constant equilibrium state (1, 0) in$$L^2$$L2-norm is$$(1+t)^{-\frac{3}{4}}$$(1+t)-34if the initial data satisfy some low-frequency assumption additionally. Furthermore, we also show that the lower bound of the$$k(k\in [1, 3])$$k(k∈[1,3])th-order spatial derivatives of solution converging to zero in$$L^2$$L2-norm is$$(1+t)^{-\frac{3+2k}{4}}$$(1+t)-3+2k4. Finally, it is proved that the lower bound of decay rate for the time derivatives of density and velocity converging to zero in$$L^2$$L2-norm is$$(1+t)^{-\frac{5}{4}}$$(1+t)-54.