In modern power systems, power transformers are considered vital components that can ensure the grid’s continuous operation. In this regard, studying the breakdown in the transformer becomes necessary, especially its insulating system. Hence, in this study, Box–Behnken design (BBD) was used to introduce a prediction model of the breakdown voltage (VBD) for the transformer insulating oil in the presence of different barrier effects for point/plane gap arrangement with alternating current (AC) voltage. Interestingly, the BBD reduces the required number of experiments and their costs to examine the barrier parameter effect on the existing insulating oil VBD. The investigated variables were the barrier location in the gap space (a/d)%, the relative permittivity of the barrier materials (εr), the hole radius in the barrier (hr), the barrier thickness (th), and the barrier inclined angle (θ). Then, only 46 experiment runs are required to build the BBD model for the five barrier variables. The BBD prediction model was verified based on the statistical study and some other experiment runs. Results explained the influence of the inclined angle of the barrier and its thickness on the VBD. The obtained results indicated that the designed BBD model provides less than a 5% residual percentage between the measured and predicted VBD. The findings illustrated the high accuracy and robustness of the proposed insulating oil breakdown voltage predictive model linked with diverse barrier effects.