We report on the observation of bulk superconductivity from dc magnetization measurements in a cylindrical single crystal of CuxBi2Se3. The magnitude of the magnetization in the Meissner state is very small and the magnetic-field dependence of the magnetization just above the lower critical field Hc1 is very different from those of usual type-II superconductors. We studied the character of the vortex state theoretically in a spin-triplet pairing superconductor and compared it with the experimental results. The results showed that, the superconductivity observed in CuxBi2Se3 is consistent with the spin-triplet pairing superconductivity with odd parity. We also observed a rapid relaxation phenomenon of the superconducting diamagnetism.