Nearly phase-pure (Hg 1 - x Re 0 . 1 )Ba 2 Ca 2 Cu 3 O 8 + δ superconducting specimens were prepared by a conventional powder-mixing and encapsulation technique. The magnetization M was measured for sintered bulk samples and for grain-aligned powders, and M is much larger for H c-axis than for H a-b plane. M decreases sharply just above the penetration field H p in the field-increasing branch. At high and moderate temperatures (T ≥ 40 K), the remanent magnetization at H = 0 is small and the M-H curves are completely asymmetric about the central line of M = 0. These features clearly show that the magnetization originates from the Bean-Livingston surface barrier. Substantial bulk pinning exists only at low temperatures, T ≥ 20 K. The magnetic hysteresis curves of Re-doped Hg-oxide samples also exhibited paramagnetism, in which a Curie-Weiss behavior occurs above T c . This paramagnetism is probably mainly carried by doped Re ions.