We present the results of a search for pair production of a fourth-generation charge −13 quark (b′) in s√=1.8TeV pp¯ collisions using 88pb−1 of data obtained with the Collider Detector at Fermilab. We assume that both quarks decay via the flavor-changing neutral current process b′→bZ0 and that the b′ mass is greater than mZ+mb. We studied the decay mode b′b′¯→Z0Z0bb¯ where one Z0 decays into e+e− or μ+μ− and the other decays hadronically, giving a signature of two leptons plus jets. An upper limit on the σpp¯→b′b′¯×[B(b′→bZ0)]2 is established as a function of the b′ mass. We exclude at 95% confidence level a b′ quark with mass between 100 and 199GeV/c2 for B(b′→bZ0)=100%.