We search for Z' bosons in dielectron events produced in pp collisions at square root of s = 1.96 TeV, using 0.45 fb(-1) of data accumulated with the Collider Detector at Fermilab II detector at the Fermilab Tevatron. To identify the Z' --> e+ e- signal, both the dielectron invariant mass distribution and the angular distribution of the electron pair are used. No evidence of a signal is found, and 95% confidence level lower limits are set on the Z' mass for several models. Limits are also placed on the mass and gauge coupling of a generic Z', as well as on the contact-interaction mass scales for different helicity structure scenarios.