This is a randomized, double-blind, active-controlled, parallel group global study designed to investigate the efficacy and safety of adding fixed-dose benralizumab (30 mg), administered subcutaneously (SC) every 4 weeks for the first 3 doses and then every 8 weeks for participants with a history of eosinophilic asthma, who remain uncontrolled on medium-dose Inhaled corticosteroid-Long-acting β2-agonists (ICS-LABA) with or without other asthma controller(s) (with the exception of oral corticosteroids), compared to the conventional treatment step of escalation of inhaled therapy to high-dose ICS-LABA plus placebo (benralizumab).