In this paper, we explore the existence of normalized solutions for the following (N, p)-Laplacian problems with exponential critical growth: \(\begin{aligned} \left\{ \begin{array}{lll} -\Delta _{p} u-\Delta _{N} u+ \mathcal {V}(\xi x)(|u|^{p-2}u+|u|^{N-2}u)=\lambda |u|^{p-2}u+\zeta f(u) \ \ \text {in} \ \mathbb {R}^{N},\\ \int _{\mathbb {R}^N} |u|^{p}dx=a^p, \end{array} \right. \end{aligned}\) where \(a,\xi>0, 2< p < N, \zeta >0\) is a suitable constant, \(\lambda \in \mathbb {R}\) is an unknown parameter that appears as a Lagrange multiplier, potential function \(\mathcal {V}: \mathbb {R}^{N}\rightarrow [0, \infty )\) is a continuous function, and f has exponential critical growth. To overcome the challenges posed by this critical growth, we adopt a truncation approach combined with variational minimization techniques. Additionally, we apply Moser iteration and \(L^\infty \) -estimate to guarantee that the solutions obtained from the truncated problem also satisfy the original equation. To some extent, we extend the results of Cai and V. D. Rădulescu [14] (J. Differential Equations, 391: 57–104, 2024), Ding et. al [20] (J. Geom. Anal. 35: Paper No. 94, 36 pp, (2025)) and Chen et al. [17] (Electron. J. Qual. Theory Differ. Equ. Paper No. 48, 19 pp, 2024).
