To address the imbalance between exploration and exploitation, slow convergence speed, premature convergence, and difficulty in escaping local optima in the Beluga whale optimization (BWO), an improved Beluga whale optimization combining dimension-by-dimension Gaussian mutation (IBWO) was proposed. Firstly, a dynamic parameter strategy was adopted to adjust the balance factor, achieving a better balance between exploration and exploitation. Secondly, the current-to-rand differential mutation operator was introduced to enhance the algorithm"s exploration capability. Then, by incorporating elite leadership strategies, the convergence speed of the algorithm was accelerated. Finally, based on the positions of the current optimal solution and the current worst solution, dimension-by-dimension Gaussian mutation was applied to the current optimal solution, thereby enhancing the algorithm"s ability to escape local optima. To validate the performance of the improved algorithm, it was compared with seven other metaheuristic algorithms on the Congress on evolutionary computation’s (CEC) 2017 test set, the experimental results demonstrate that IBWO exhibits superior optimization capabilities compared to other algorithms. Appling IBWO to three engineering problems, the results show that IBWO performs well in solving complex real-world optimization problems.