The plasma membrane has heterogeneity, where the constituents are not only asymmetrically distributed between the inner leaflet and the outer leaflet but also laterally organized within each leaflet. There is still an ongoing controversy over the cholesterol distribution between the two leaflets, and it is also significant to explore the lateral flow and localization of cholesterol. The unilamellar vesicle is extensively employed as a simplified model of the plasma membrane in research studies. In this work, we study the spontaneous spatial distribution of cholesterol in the small unilamellar vesicles with a single type of phospholipid as the bilayer backbone through coarse-grained molecular dynamics simulations. The results show that in a spherical vesicle under ambient pressure, cholesterol is more abundant in the inner leaflet than in the outer leaflet. As the vesicle is deformed under pressurization, the net lateral flow of cholesterol in the two leaflets is in the exactly opposite directions, finally leading to a distribution strongly associated with the monolayer curvature. One of the possible explanations for our results is from the point of view of curvature elastic energy. Another possibility is from the point of view of stress: according to the correlation between the cholesterol distribution and the tail angles of lipids, it is suggested that the possible governing mechanism for the distribution of cholesterol in a membrane is to alleviate the mismatch of stress between the two leaflets. Additionally, we obtain the effect of cholesterol infiltration on the bending modulus and the spontaneous curvature of the vesicles.