Production of galactooligosaccharides by an immobilized $eta$-galactosidase from Aspergillus niger CAD 1 in sodium alginate was investigated. The ranges of temperature and pH for the maximum stability of im-mobilized $eta$-galactosidase were 20~45$^{circ}C$ and 4.0~5.5, respectively. The activation energy for the immob-illized $eta$-galactosidase was 13,400 cal/mole At the concentration of the immobilized $eta$-galactosidase 0.12 unit/g in sodium alginate the yield of galactooligosaccharides in cheese whey containing 20% lactose was 18% after incubation for 72 hr at 45$^{circ}C$. The remaining activity for the immobilized $eta$-galactosidase 10 times repeated use 87%.