Bin packing problem (BPP) is a classical combinatorial optimization problem widely used in a wide range of fields. The main aim of this paper is to propose a new variant of whale optimization algorithm named improved Lévy-based whale optimization algorithm (ILWOA). The proposed ILWOA adapts it to search the combinatorial search space of BPP problems. The performance of ILWOA is evaluated through two experiments on benchmarks with varying difficulty and BPP case studies. The experimental results confirm the prosperity of the proposed algorithm in proficiency to find the optimal solution and convergence speed. Further, the obtained results are discussed and analyzed according to the problem size.