It has been found that a cyclodextrin derivative, 2-hydroxypropyl-β-cyclodextrin (HPβCD), has reasonable therapeutic effect on Niemann-Pick disease type C, which is caused by abnormal accumulation of unesterified cholesterol and glycolipids in the lysosomes and shortage of esterified cholesterol in other cellular compartments. We study the binding affinity and mode of HPβCD with cholesterol to elucidate the possible mechanism of HPβCD for removing cholesterol from the lysosomes. The dominant binding mode of HPβCD with cholesterol is found based on the molecular dynamics simulation and a statistical mechanics theory of liquids, or the three-dimensional reference interaction site model theory with Kovalenko-Hirata closure relation. We examine the two types of complexes between HPβCD and cholesterol, namely, one-to-one (1:1) and two-to-one (2:1). It is predicted that the 1:1 complex makes two or three types of stable binding mode in solution, in which the βCD ring tends to be located at the edge of the steroid skeleton. For the 2:1 complex, there are four different types of the complex conceivable, depending on the orientation between the two HPβCDs: head-to-head (HH), head-to-tail (HT), tail-to-head (TH), and tail-to-tail (TT). The HT and HH cyclodextrin dimers show higher affinity to cholesterol compared to the other dimers and to all the binding modes of 1:1 complexes. The physical reason why the HT and HH dimers have higher affinity compared to the other complexes is discussed based on the consistency with the 1:1 complex. On the one hand, in case of the HT and HH dimers, the position of each CD in the dimer along the cholesterol chain comes right on or close to one of the positions where a single CD makes a stable complex. On the other hand, one of the CD molecules is located on unstable region along the cholesterol chain, for the case of TH and TT dimers.