In this study, a new apparatus for measuring the air permeability of wood-based panel specimens without using water displacement was developed with the aim of decreasing the influence of variation in atmospheric pressure on permeability measurement. Validation experiments were conducted using plywood, oriented strand board (OSB), particleboard, and medium-density fiberboard (MDF) panels and a control specimen sealed with an epoxy resin. The background (leakage) flow of the apparatus was evaluated based on the experimental results of the control specimen. A methodology for the determination of air permeability based on Darcy’s law for gases and the evaluated background flow rate was proposed. The results of the current study were compared with those obtained in a previous study, indicating that the new method provides valid measurements for wood-based panels with high and low air permeability. No significant influence of variation in atmospheric pressure on the experimental results was observed, suggesting that the proposed method is suitable for a long-term continuous experiment for evaluating a specimen with extremely low permeability.