The present study describes the production of the value-added chemical 1,3-propanediol (1,3-PD) from crude glycerol, a waste by-product formed during biodiesel production. The efficiency, robustness, and stability of the process were improved by immobilization of the anaerobic bacterium Clostridium butyricum into a polyvinyl alcohol (PVA) hydrogel. The highest average productivity, 6.8 ± 0.2 g/(L·h), was achieved in 10 consecutive, repeated batch fermentations, with an initial concentration of pure glycerol 45.5 ± 0.7 g/L, after 2.5 hours. The highest final concentration and yield of 1,3-PD, 28.3 ± 0.6 g/L, and 0.42 ± 0.01 g/g, respectively, were achieved in eleven repeated batch fermentations, after increasing the initial pure glycerol concentration to 70.4 ± 1.9 g/L. Two different types of crude glycerol, produced from used cooking oil (UCO) and rapeseed oil (RO), were tested in repeated batch fermentations, with an average productivity achieved of 2.3 ± 0.1 and 3.5 ± 0.3 g/(L·h), respectively. The highest final concentration and yield of 1,3-PD, 12.6 ± 0.9 g/L, and 0.35 ± 0.02 g/g, respectively, were observed in fifteen repeated batch fermentations with RO crude glycerol. An excellent stability of the immobilized anaerobic bacteria and increase of productivity in fermentation of crude glycerol was demonstrated.