A hydrogen sulfide scrubber includes first and second scrubber tanks with scrubber media contained therein. Scrubbing solution circulators each include a dispenser for dispensing scrubbing solution into contact with the scrubber media, a sump for collecting the scrubbing solution after contact with the scrubber media, and a circulating pump for circulating the scrubbing solution from the sump back to the dispenser after contact with the scrubber media. A polymeric amine supply is provided for supplying a polymeric amine to the scrubbing solution in the second tank. The scrubbing solution in the first tank may be charged with the polymeric amine by a charging line extending from the second tank to the first tank. In other embodiments, a regenerative blower and associated nozzle may be used to generate a scrubbing solution mist in the space beneath the scrubber media and above the sump.