Gluon bremsstrahlung induced by multiple parton scattering in a finite dense medium has a unique angular distribution with respect to the initial parton direction. A dead-cone structure with an opening angle \theta2_0 \approx 2(1-z)/(zLE) for gluons with fractional energy z arises from the Landau-Pomeran chuck-Migdal (LPM)interference. In a medium where the gluon's dielectric constant is \epsilon >1, the LPM interference pattern is shown to become Cherenkov-like with an increased opening angle determined by the dielectric constant $\cos2\theta_c=z+(1-z)/\epsilon$. For a large dielectric constant \epsilon \gg 1+2/z2LE, the corresponding total radiative parton energy loss is about twice that from normal gluon bremsstrahlung. Implications of this Cherenkov-like gluon bremsstrahlung to the jet correlation pattern in high-energy heavy-ion collisions is discussed.