We have searched for heavy neutral gauge bosons (Z′) in dielectron and dimuon decay modes using 110pb−1 of ¯pp collisions at √s=1.8TeV collected with the Collider Detector at Fermilab. We present a limit on the production cross section times branching ratio of a Z′ boson decaying into dileptons as a function of Z′ mass. For mass MZ′>600GeV/c2, the upper limit is 40 fb at 95% confidence level. We set the lower mass limits of 690, 590, 620, 595, 565, 630, and 600GeV/c2 for Z′SM, Zψ, Zη, Zχ, ZI, ZLR, and ZALRM, respectively.