A new complex programming problem, i.e., Interval-valued trapezoidal neutrosophic multi-level multiobjective linear programming problem (IV-TrN-ML-MOLPP), in which the coefficients/parameters of the programming problems are in the mathematical representation \( \Big(\tilde{a}=\left\langle \left({a}_1,\kern0.5em {a}_2,\kern0.5em {a}_3,\kern0.5em {a}_4\right)\right.; \) \( \left.\left[{\mu}_{\tilde{a}}^L,{\mu}_{\tilde{a}}^U\right],\Big[{\sigma}_{\tilde{a}}^L,{\sigma}_{\tilde{a}}^U\Big],\Big[{\upsilon}_{\tilde{a}}^L,{\upsilon}_{\tilde{a}}^U\Big]\right\rangle \) of interval-valued trapezoidal neutrosophic numbers (IV-TrNNs) is highlighted in this paper, and a unique solution methodology based on the accuracy function values of neutrosophic numbers is proposed. In the intended work, the IV-TrN-ML-MOLP problem is converted into an equivalent crisp problem using the accuracy function of each N coefficient/parameter of the problem. Thereafter, the multi-level and multiobjective part of the problem is tackled by creating a linear membership function for each objective function and decision variables up to (T-1) levels of the crisp problem. Then, the usual goal programming is applied to formulate the solution model to obtain a satisfactory solution to the original IV-TrN-ML-MOLPP. A numerical example is illustrated stepwise to show the applicability of the proposed technique.