We have studied one-hole dynamics in a quantum antiferromagnet by use of the anisotropic three-dimensional t-J model in the simple cubic lattice within the self-consistent Born approximation. The hole spectral function, the density of states, the quasiparticle dispersion relationship, the effective mass, the quasiparticle spectral weight, and the incoherent multiple spin-wave background are determined as functions of the Heisenberg exchange and hopping amplitude in the thermodynamic limit.