We report on results from Suzaku broadband X-ray observations of the southwest part of the Galactic supernova remnant ( SNR ) RX J1713.7 - 3946 with an energy coverage of 0.4–40 keV . The X-ray spectrum , presumably of synchrotron origin , is known to be completely lineless , making this SNR ideally suited for a detailed study of the X-ray spectral shape formed through efficient particle acceleration at high speed shocks . With a sensitive hard X-ray measurement from the HXD PIN on board Suzaku , we determine the hard X-ray spectrum in the 12–40 keV range to be described by a power law with photon index \Gamma = 3.2 \pm 0.2 , significantly steeper than the soft X-ray index of \Gamma = 2.4 \pm 0.05 measured previously with ASCA and other missions . We find that a simple power law fails to describe the full spectral range of 0.4–40 keV and instead a power-law with an exponential cutoff with hard index \Gamma = 1.50 \pm 0.09 and high-energy cutoff \epsilon _ { c } = 1.2 \pm 0.3 keV formally provides an excellent fit over the full bandpass . If we use the so-called SRCUT model , as an alternative model , it gives the best-fit rolloff energy of \epsilon _ { roll } = 0.95 \pm 0.04 keV . Together with the TeV \gamma -ray spectrum ranging from 0.3 to 100 TeV obtained recently by HESS observations , our Suzaku observations of RX J1713.7 - 3946 provide stringent constraints on the highest energy particles accelerated in a supernova shock .