We investigate the gauge/gravity duality between the $$\mathcal{N} = 6$$ $N=6$ mass-deformed ABJM theory with $$\hbox {U}_k(N)\times \hbox {U}_{-k}(N)$$ ${\text{U}}_k\left(N\right)\times {\text{U}}_{-k}\left(N\right)$ gauge symmetry and the 11-dimensional supergravity on LLM geometries with SO(2,1)$$\times $$ $\times$ SO(4)/$${\mathbb {Z}}_k$$ $Z_k$ $$\times $$ $\times$ SO(4)/$${\mathbb {Z}}_k$$ $Z_k$ isometry, in terms of a KK holography, which involves quadratic order field redefinitions. We establish the quadratic order KK mappings for various gauge invariant fields in order to obtain the canonical 4-dimensional gravity equations of motion and to reduce the LLM solutions to an asymptotically AdS$$_4$$ ${}_4$ gravity solutions. The non-linearity of the KK maps indicates that we can observe the true purpose of the non-linear KK holography of the LLM solutions. We read the vacuum expectation value of conformal dimension two operator from the asymptotically AdS$$_4$$ ${}_4$ gravity solutions. For the LLM solutions which are represented by square-shaped Young diagrams, we compare the vacuum expectation value obtained from the holographic procedure with the result obtained from the field theory, which is given by $$\langle \mathcal{O}^{(\Delta =2)}\rangle =\sqrt{k}N^{\frac{3}{2}}f_{(\Delta =2)}+\mathcal{O}(N)$$ $⟨O^{(\Delta =2)}⟩=\sqrt{k}{N}^{\frac{3}{2}}{f}_{(\Delta =2)}+O\left(N\right)$ , where $$f_{\Delta }$$ $f_{\Delta }$ is independent of N. Based on this result, we examine the gauge/gravity duality in the large N limit and finite k. We also show that the vacuum expectation values of the massive KK graviton modes are vanishing as expected by the supersymmetry.