The fastest-rotating magnetar 1E 1547.0-5408 was observed in broad-band X-rays with Suzaku for 33 ks on 2009 January 28-29, 7 days after the onset of its latest bursting activity. After removing burst events, the absorption-uncorrected 2-10 keV flux of the persistent emission was measured with the XIS as 5.7e-11 ergs cm-2 s-1, which is 1-2 orders of magnitude higher than was measured in 2006 and 2007 when the source was less active. The persistent emission was also detected significantly with the HXD in >10 keV up to at least ~110 keV, with an even higher flux of 1.3e-10 ergs cm-2 s-1 in 20-100 keV. The pulsation was detected at least up to 70 keV at a period of 2.072135+/-0.00005 s, with a deeper modulation than was measured in a fainter state. The phase-averaged 0.7-114 keV spectrum was reproduced by an absorbed blackbody emission with a temperature of 0.65+/-0.02 keV, plus a hard power-law with a photon index of ~1.5. At a distance of 9 kpc, the bolometric luminosity of the blackbody and the 2-100 keV luminosity of the hard power-law are estimated as (6.2+/-1.2)e+35 ergs s-1 and 1.9e+36 ergs s-1, respectively, while the blackbody radius becomes ~5 km. Although the source had not been detected significantly in hard X-rays during the past fainter states, a comparison of the present and past spectra in energies below 10 keV suggests that the hard component is more enhanced than the soft X-ray component during the persistent activity.