The film growth of He-4 adsorbed in mesoporous substrates was investigated by accurate vapor pressure measurements for various pore sizes between 18 Angstrom and 47 Angstrom. The He-4 film adsorbed on the pore wall forms a cylindrical tube, but does not show the capillary condensation. Completion of the first layer and the full pore coverage could be identified for all pore sizes studied. In the first layer, no pore size dependence of the film growth was found, indicating that the growth of this layer was dominated primarily by the van der Waals force from the substrate. Film growth after the first layer completion, however, has a strong pore size dependence. The ratio of the first layer completion and the full pore coverage agrees well with that expected from the pore dimensions.