BACKGROUND In recent years, the discharge of heavy metal ions in natural waters has become a serious problem. Among the various techniques that have been employed for heavy metal removal, adsorption is highly effective and economical because low‐cost adsorbents can be employed. Brown algae are a potential biosorbent because of their high uptake capacities for various heavy metal ions. Petalonia fascia biomass immobilized in an agar matrix was tested as a new removal agent of MoVI from contaminated waters. RESULTS Sorption studies were performed in batch and continuous systems. Petalonia fascia has a high adsorption capacity (1376 ± 2 mg g−1) at 20 °C and pH 1.0. Participation of hydroxyl and carboxylate functional groups in the adsorption of molybdate anions was confirmed by FT‐IR analysis. SEM images showed that morphological surface changes happen after MoVI sorption. Mean free energies of sorption and activation parameters demonstrate that the sorption mechanism was chemical sorption. MoVI sorption onto brown seaweed surface was spontaneous and exothermic. Petalonia fascia has an energetically heterogeneous surface. Continuous sorption data were best fitted by a modified dose–response model. Scale‐up of the sorption processes was achieved applying a bed depth service time (BDST) model. The critical bed depth, Z0 was 1.7 cm. CONCLUSIONS Petalonia fascia biomass is a good adsorbent material for MoVI and it can be used in fixed bed columns for the purification of MoVI contaminated effluents. The high value of qmax and the low cost of this seaweed make this biomass a good sorbent for use in continuous treatment of groundwater and effluents contaminated with molybdate anions. © 2016 Society of Chemical Industry