In this study, we investigated the quantization of magnetization at low temperatures in a spin-1 antiferromagnetic chain with single-ion anisotropy by considering the quenched disorder in alternating bonds. Each spin i interacts with its nearest neighbors via Ji and αJi couplings, where Ji is considered to obey a Gaussian or Bernoulli probability distribution function, with width σ. Zero temperature phase diagrams were obtained by minimizing the energy of the Hamiltonian. For finite temperatures, a transfer matrix technique was applied in order to treat the partition function. Consequently, the magnetization curve calculated by deriving the quenched average of the free energy exhibited interesting plateaus, which were modified when randomness was considered. Experimentally, these plateaus appear when some chain structures are subjected to a magnetic field.