Context. IGR J17511-3057 is the second X-ray transient accreting millisecond pulsar discovered by INTEGRAL. It was in outburst for about a month beginning on September 13, 2009. Aims: We analyze the spectral and timing properties of the object and the characteristics of X-ray bursts with the aim to constrain the physical processes responsible for the X-ray production in this class of sources. Methods: We studied the broad-band spectrum of the persistent emission in the 0.8-300 keV energy band using simultaneous INTEGRAL, RXTE and Swift data obtained in September 2009. We also describe the timing properties in the 2-120 keV energy range such as the outburst light curve, pulse profile, pulsed fraction, pulsed emission, and time lags, and moreover study the properties of X-ray bursts discovered by RXTE and INTEGRAL and the recurrence time. Results: The broad-band average spectrum is well described by thermal Comptonization with an electron temperature of kTe ~ 25 keV, soft seed photons of kTbb ~ 0.6 keV, and Thomson optical depth τT ~ 2 in a slab geometry. During the outburst the spectrum stays remarkably stable with plasma and soft seed photon temperatures and scattering optical depth being constant within errors. We fitted the outburst profile with the exponential model, and using the disk instability model we inferred the outer disk radius to be (4.8-5.4) × 1010 cm. The INTEGRAL and RXTE data reveal the X-ray pulsation at a period of 4.08 milliseconds up to ~120 keV. The pulsed fraction is shown to decrease from ~22% at 3 keV to a constant pulsed fraction of ~17-18% between 7-30 keV, and then to decrease again to ~13% at 60 keV. The nearly sinusoidal pulses show soft lags that monotonically increase with energy to about 0.2 ms at 10-20 keV similar to those observed in other accreting pulsars. The short burst profiles indicate hydrogen-poor material at ignition, which suggests either that the accreted material is hydrogen-deficient, or that the CNO metallicity is up to a factor of 2 times solar. However, the variation of the burst recurrence time as a function of ṁ (inferred from the X-ray flux) is much smaller than predicted by helium-ignition models.