Developing novel methanol-feeding strategies for the improved production of heterologous proteins in high cell-density fed-batch cultures of Pichia pastoris has been of great interest during recent years. In this study, a recombinant P. pastoris strain (GS115/$His^+;Mut^+$) producing ${eta}$-galactosidase (${eta}$-Gal) was used to investigate conventional feeding strategies and to develop a new strategy to increase the recombinant protein production during fed-batch cultures on methanol. Three types of conventional methanol-feeding strategies, including ${mu}$-stat, dissolved oxygen-stat (DO-stat) and constant methanol concentration were investigated and compared with respect to alcohol oxidase (AOX), formate dehydrogenase (FDH) and ${eta}$-gal activities, and cell dry weight (CDW), methanol, and formaldehyde concentration variations during the production phase. Methanol feeding with ${mu}$-stat 0.025/h exhibited the highest ${eta}$-gal activity. Supplementing ammonium and magnesium in ${eta}$-stat 0.025/h did not affect the cell growth or methanol or formaldehyde concentrations throughout the fermentation but did improved the maximum ${eta}$-gal activity from 148.2 to 158.1 kU/mL. A new three-step methanol-feeding strategy was developed based on the results obtained from conventional feeding strategies, which started with ${mu}$-stat 0.025/h for 5 h, then ${eta}$-stat 0.030/h, and finally, was switched to DO-stat when maintaining the DO above 20% air saturation became difficult. Implementation of this new feeding strategy resulted in a CDW of $107.2{pm}0.7$ g/L, AOX specific activity of $0.1890{pm}0.0030$ U/mg CDW, and ${eta}$-gal activity of $173.5{pm}2.1$ kU/mL after 29 h of fermentation, which shows a 5.6, 29.1, and 15.7% increase in CDW, AOX, and ${eta}$-gal activity, respectively, compared to that of ${mu}$-stat at 0.025/h.