${eta}$-Galactosidase was immobilized on chitosan bead by covalent bonding using glutaraldehyde. The characteristics of the immobilized enzyme were investigated. Maximum immobilization yield of 75% was obtained on chitosan bead. Optimum pH and temperature for the immobilized enzyme was 7.0 and $50^{circ}C$, respectively. The immobilized enzyme showed a broader range of pH and temperature compared to a free one. A mathematical model for the operation of the immobilized enzyme in a packed-bed reactor was established and solved numerically. Under different inlet lactose concentrations and feed flow rate conditions, lactose conversion was measured in a packed-bed reactor. The experimental results of continuous operation in a packed-bed reactor were compared to theoretic results using Michaelis-Menten kinetics with competitive product inhibition and external mass transfer resistance. The model predicted the experimental data with errors less than 5%. Process optimization of continuous operation in a packed-bed reactor was also conducted. In a recirculation packed-bed operation, conversion of lactose was 97% in 3 hours. In a continuous packed-bed operation, the effect of flow rate and initial lactose concentration was investigated. Increasing flow rates and initial lactose concentration decreased the conversion of substrate.