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This study presents a temporal and spectral analysis of the prompt emission of two high-redshift gamma-ray bursts (GRBs), 120521C at z ∼ 6 and 130606A at z ∼ 5.91, using data obtained from the Swift-XRT/BAT and the Suzaku-WAM simultaneously. Based on follow-up XRT observations, the longest durations of the prompt emissions were approximately 80 s (120521C) and 360 s (130606A) in the rest-frames of the two GRBs. These objects are thus categorized as long-duration GRBs; however, the durations are short compared with the predicted duration of GRBs originating from first-generation stars. Because of the wide bandpass of the instruments, covering the ranges 15 keV-5 MeV (BAT-WAM) and 0.3 keV-5.0 MeV (XRT-BAT-WAM), we could successfully determine the νF_ν peak energies E_ peak_^ src^ in the rest-frame and isotropic-equivalent radiated energies E_iso; E^ src^_ peak_ = 682⁺⁸⁴⁵_–207 keV and E_ iso_ = (8. 25^+2.24_–1.96) ×10⁵² erg for 120521C, and E^ src^_ peak_ = 1209⁺⁵⁵³_–304 keV and E_ iso_ = (2.82^+0.17_–0.71) ×10⁵³ erg for 130606A. These obtained characteristic parameters are in accordance with the well-known relationship between E_ peak_^ src^ and E_iso (Amati relationship). In addition, we examined the relationships between E_ peak_^ src^ and the 1-s peak luminosity, L_p, and between E_ peak_^ src^ and the geometrical corrected radiated energy, E_γ, and confirmed the E_ peak_^ src^-L_p (Yonetoku) and E_ peak_^ src^-E_γ (Ghirlanda) relationships. The results imply that these high-redshift GRBs at z ∼ 6, which are expected to have radiated during the reionization epoch, have properties similar to those of low-redshift GRBs regarding X-ray prompt emission.