We demonstrate sub-Doppler cooling of rubidium (87Rb) atoms using a compact, single-beam configuration based on a conical hollow mirror integrated with anti-Helmholtz coils. The conical geometry converts a single incident beam into an effective six-beam magneto-optical trap (MOT) configuration while focusing the light towards the cone axis, thereby reducing the required laser power. The number of atoms in the conical MOT is maximized at an incident intensity of 6.5 mW/cm2 in our conical MOT, several times lower than in conventional six-beam MOTs. Under optimal conditions, we trap ~1 x 10^7 87Rb atoms. We obtain sub-Doppler temperature of Tr = 13.4 +/- 1.2 µK and Tz = 106 +/- 11 µK by polarization gradient cooling (PGC), revealing a strong anisotropy that we attribute to the polarization pattern created by the conical mirror. In addition, a modified release-and-recapture measurement in the MOT yields a radial temperature Tr = 1.20 +/- 0.02 mK, approximately five times higher than that expected for comparable light-shift parameters in a six-beam MOT, in agreement with previous simulations. Our results establish conical hollow mirrors as a practical and power-efficient platform for compact cold-atom sources and integrated quantum sensors.