A scaling up study for the exopolysaccharide (EPS) production by submerged culture of Ganoderma lucidum was carried out in jar fermenter systems (2.6, 20 and 75 L) under bi-staged pH process. Profiles of dissolved oxygen (DO) and volumetric coefficient of oxygen transfer ($k_La$) as a function of operating variables (agitation speed and aeration rate) was investigated, and a correlation between $k_La$ and operating variables was analysed statistically. Under bi-staged pH process, no limitation of DO was observed at agitation speeds tested in the range of 200 and 600 rpm, and the highest EPS production was obtained at the level of DO of $40{sim}80%$. From the regression analysis, the relation between $k_La$, gas velocity (Vs), stirrer speed (N) and impeller diameter (Di) could be expressed as : $$k_La=0.555{ imes}Vs^{0.42}{ imes}(N^3{ imes}Di^2)^{0.33};(R^2=0.925,;p < 0.05)$$ It was found that under 2.6 L jar fermenter, the optimum agitation speed and aeration rate was 400 rpm and 1 vvm, respectively, obtaining the EPS production of 15.43 g/L. Under the submerged cultivation of G. lucidum in jar fermenters of $2.6{sim}75;L$, the similar EPS yields at each fermenter were achieved during scaling up based on $k_La$, and $k_La$ value for maximum EPS production was $85.4{pm}26.70;h^{-1}$.