Narrow-band terahertz (THz) Cherenkov radiation can be excited as a relativistic electron bunch passes through the dielectric capillary with sub-millimeter radius. However, due to the diffraction effect, the radiation will enter free space with a large divergence angle, which makes it difficult to collect the radiation energy efficiently. In this Letter, to deal with this challenge, we propose to add a new dielectric layer, which satisfies a special relationship with the electron velocity, between the metal coating and original dielectric layer in the capillary. According to numerical simulation and theoretical analysis results, the divergence angle of radiation is significantly suppressed, and the peak power density is also enhanced by over two orders. As a result, the transmission efficiency from the radiation source to the optical system can be increased to over 90%. We expect that this method will provide a new way to generate THz Cherenkov radiation.