The radiation from a moving point charge in an anisotropic cold plasma drifting uniformly along a finite external magnetic field is investigated. It is assumed that the charge is moving uniformly in the direction of the external magnetic field. In general, the radiation consists of two waves, i.e., the ordinary and extraordinary waves. The effects of the drift motion of the background plasma on the radiation characteristics of both waves are discussed in detail. It is found that as the drift velocity of the plasma increases and approaches that of the moving source, the radiated energy of the ordinary wave is resonantly enhanced and the Cerenkov ray becomes concentrated in the direction of the motion of the source.