Studies on hydrogen leakage have mainly focused on the influences of location and geometrical configuration on the distribution of the hydrogen in various spaces. The present study developed a simplified model for the leakage diffusion of hydrogen in an enclosed cuboid space with two vents, at the top and at the bottom, respectively. The effect of different leakage positions on the diffusion of the hydrogen was analyzed. The results showed that when hydrogen diffused vertically from the bottom to the top of the space, the farther the leakage position was from the vent on the side wall, the more hydrogen accumulated. When the hydrogen leaked in the vertical direction from the floor, the distance between the leakage position and the bottom vent had little effect on the horizontal diffusion speed of the hydrogen at the top of the space. The diffusion speed for the leakage in the horizontal direction was faster than that in the vertical direction. When the hydrogen leaked in the horizontal direction from the side wall, the height of the leakage had little effect on the horizontal diffusion speed of the hydrogen at the top of the space. Stratification occurred for models set up in the present study whenever the envelope of 1% mole fraction, or 4% mole fraction, of hydrogen extended to the whole ceiling.