We present the Suzaku results of eta Carinae in the 5-50 keV range conducted twice around the apastron in 2005 August for 50 ks and in 2006 February for 20 ks. The X-ray Imaging Spectrometer (XIS) produced hard (5-12 keV) band spectra, resolving K shell lines from highly ionized Fe and Ni. The Hard X-ray Detector yielded a significant detection in the super-hard (15-50 keV) band, which was uncontaminated by near-by sources. We constrained the temperature of the optically thin thermal plasma emission dominant in the hard band to be 3-4 keV using the K-shell line features with the XIS. We found significant excess emission above the thermal emission in the super-hard band with the PIN, confirming the previous INTEGRAL ISGRI report. The entire 5-50 keV spectra were fitted by a combination of a thermal plasma model plus a flat power-law, or a very hot thermal bremsstrahlung model for the excess emission. No significant change of the excess emission was found at different epochs within the systematic and statistical uncertainties, and no flare-like flux amplification was seen in the hard band, indicating that the excess emission is a steady phenomenon. We argue that the super-hard emission is attributable to the inverse Compton of stellar UV photons by non-thermal electrons or to the thermal bremsstrahlung of very hot plasma, and not to the bremsstrahlung by non-thermal electrons colliding with cold ambient matter.