We use polarized inelastic neutron scattering (INS) to study spin excitations of optimally holedoped superconductor Ba0.67K0.33Fe2As2 (Tc = 38 K). In the normal state, the imaginary part of the dynamic susceptibility, χ ′′ (Q, ω), shows magnetic anisotropy for energies below ∼7 meV with c-axis polarized spin excitations larger than that of the in-plane component. Upon entering into the superconducting state, previous unpolarized INS experiments have shown that spin gaps at ∼5 and 0.75 meV open at wave vectors Q = (0.5, 0.5, 0) and (0.5, 0.5, 1), respectively, with a broad neutron spin resonance at Er = 15 meV. Our neutron polarization analysis reveals that the large difference in spin gaps is purely due to different spin gaps in the c-axis and in-plane polarized spin excitations, resulting resonance with different energy widths for the c-axis and in-plane spin excitations. The observation of spin anisotropy in both opitmally electron and hole-doped BaFe2As2 is due to their proximity to the AF ordered BaFe2As2 where spin anisotropy exists below TN .