Palm kernel cake (PKC), is an agro-industrial residue created in the palm oil industry, and large quantities of PKC are produced in Malaysia. Sustainable development of the palm oil industry in Malaysia demands an economical technology for the environmentally friendly utilization of PKC in industrial utility systems. This research was carried out to evaluate the use of PKC in the production of cellulase by the cultivation of Aspergillus niger FTCC 5003 in a laboratory packed-bed bioreactor for seven days. A central composite design was used to perform eighteen trials of solid substrate fermentation under selected conditions of incubation temperature, initial moisture content of substrate, and airflow rate. Experimental results showed that a cellulase yield of 244.53 U/g of dry PKC was obtained when 100 g of PKC was hydrolyzed at an incubation temperature of $32.5^{circ}C$, an initial moisture level of 60%, and an aeration rate of 1.5 L/min/g PKC. An empirical second-order polynomial model was adjusted to the experimental data to evaluate the effects of the studied operating variables on cellulase production. The statistical model revealed that the quadratic term for initial moisture content had a significant effect on the production of cellulase (P < 0.01). The regression model also indicated that the quadratic terms for incubation temperature and interaction effects between initial moisture content and aeration rate significantly influenced cellulase production (P < 0.05). The empirical model determined that the optimum conditions for cellulase production were an incubation temperature of $31.0^{circ}C$, an initial moisture content of 59.0% and an airflow rate of 1.55 L/min/g PKC.