Display omitted •Use of constitutive PGK promoter for CalB production in Pichia pastoris.•Study of specific growth rate effect in CalB production by Pichia pastoris.•Comparison between chemostat and fed-batch culture modes.•Theoretical best operational strategy over a 6-weeks period. In this work, continuous and fed-batch operational modes for producing the recombinant protein lipase B from Candida antarctica under the new constitutive promoter PGK in the cell factory Pichia pastoris was assessed. For this purpose, the influence of the specific growth rate (μ) was examined from 0.05 to 0.16 h−1 on various key bioprocess parameters. The overall biomass-to-substrate yield YX/S and specific substrate uptake rate (qs) were found to be independent of the particular operational mode. However, the μ-dependence of specific production rate (qp) differed with the cultivation strategy used. Thus, qp was linearly related in the continuous mode but suggested saturation in fed-batch cultures. The highest volumetric and specific productivity were obtained at the highest μlevels in the continuous mode, which provided volumetric and specific productivities (QP and Qe, respectively) roughly 1.5 and 3 times greater than the fed-batch mode. The continuous mode also proved more effective in the long rung; thus, CalB production after 6 weeks was estimated to be about 5.8 times greater than with the fed-batch mode. Continuous operation with the novel constitutive promoter PGK is thus a realistic alternative to the standard fed-batch cultivation at a high cell density typically used in industrial bioprocesses for heterologous protein production in Pichia pastoris.