Gamow-Teller (GT) transitions starting from the T-z = +2 nucleus Zn-64 to the T-z = +1 nucleus Ga-64 were studied in a (p, n)-type (He-3,t) charge-exchange reaction at a beam energy of 140 MeV/nucleon and scattering angles close to 0 degrees. Here, T-z is the z component of the isospin T. The experiment was conducted at the Research Center for Nuclear Physics (RCNP) in Osaka, Japan. An energy resolution of approximate to 34 keV was achieved by applying beam matching techniques to the Grand Raiden magnetic spectrometer system. With our good resolution, we could observe GT strength fragmented in many states up to an excitation energy of approximate to 11 MeV. By performing angular distribution analysis, we could identify states in Ga-64 excited by GT transitions. The reduced GT transition strengths [B(GT)values] were calculated assuming the proportionality between the cross sections and the B(GT)values. Shell-model calculations using the GXPF1J interaction reproduced the B(GT)strength distribution throughout the spectrum. States with isospin T = 3 were identified by comparing the Zn-64(He-3,t)Ga-64 spectrum with a Zn-64(d, He-2)Cu-64 spectrum. Relative excitation energies of the corresponding structures are in good agreement, supporting the robustness of isospin symmetry in the mass number A = 64 nuclei.