Using data from proton-antiproton collisions at Ecms=1.96 TeV recorded by the CDF II detector at the Fermilab Tevatron, evidence for the excited resonance state Lambda_b* is presented in its Lambda_b0 pi+ pi- decay, followed by the Lambda_b0 --Lambda_c+ (--proton K- pi+) pi- decays. The analysis is based on a data sample corresponding to an integrated luminosity of 9.6/fb collected by an online event selection based on charged-particle tracks displaced from the proton-antiproton interaction point. The significance of the observed signal is 3.5 Gaussian sigmas. The mass of the observed state is found to be 5919.22 +- 0.76 MeV in agreement with similar findings in proton-proton collision experiments.