A method and a plant to remove metals by biosorption from mining or industrial effluents comprising: (a) subject the effluent to at least one first stage of pre-treatment, selecting among: precipitation by pH rising, solvent extraction or solvent extraction on emulsified membranes in order to reduce its load of metals to a concentration level that allows it to be treated by the next stage of biosorption, and (b) subject the liquid that has been previously in the stage of pre-treatment to a second stage of continuous metals removal by biosorption. To perform the continuous metals removal by biosorption is supplied a group of reactors, constituted for at least one, or at least two or at least three fixed bed bioreactors, which packing material has been colonized with a biofilm formed by a bacterial culture or a mixture of microorganisms with the capacity of binding metals by biosorption; pre-treated water is led to the group of bioreactors, the treated effluent comes from this last one and is led to the discharge of the plant.