A distinct peak is observed in the pi(+/-)psi' invariant mass distribution near 4.43 GeV in B -> K pi(+/-)psi' decays. A fit using a Breit-Wigner resonance shape yields a peak mass and width of M=4433 +/- 4(stat)+/- 2(syst) MeV and Gamma=45(-13)(+18)(stat