Context. The unknown identity of the diffuse interstellar band (DIB) carriers poses one of the longest standing unresolved problems in astrophysics. While the presence, properties, and behaviour of hundreds of optical DIBs between 4000 Å and 9000 Å have been well established, information on DIBs in both the ultra-violet and near-infrared (NIR) ranges is limited. Aims. In this paper, we present a spectral survey of the NIR range, from 0.9 µm to 2.5 µm. Our observations were designed to detect new DIBs, confirm previously proposed NIR DIBs, and characterise their behaviour with respect to known line-of-sight properties (including the optical DIBs present in our spectra). Methods. Using the X-Shooter instrument mounted on the ESO Very Large Telescope (VLT) we obtained medium-resolution spectra of eight known DIB targets and one telluric reference star, from 3000 Å to 25 000 Å in one shot.Results. In addition to the known 9577, 9632, 10 780, 11 797, and 13 175 Å NIR DIBs, we confirm 9 out of the 13 NIR DIBs that were presented by Geballe et al. (2011, Nature, 479, 200). Furthermore, we report 11 new NIR DIB candidates. The strengths of the strongest NIR DIBs show a general correlation with reddening, E (B − V) , but with a large scatter. Several NIR DIBs are more strongly correlated with the 5780 Å DIB strength than with E (B − V) ; this is especially the case for the 15 268 Å DIB. The NIR DIBs are strong: the summed equivalent widths of the five strongest NIR DIBs represent a small percent of the total equivalent width of the entire average DIB spectrum (per unit reddening). The NIR DIBs towards the translucent cloud HD 147889 are all weak with respect to the general trend. No direct match was found between observed NIR DIBs and laboratory matrix-isolation spectroscopic data of polycyclic aromatic hydrocarbons (PAHs). Conclusions. The strong correlation between the 5780−15 268 DIB pair implies that (N f ) 5780 /(N f ) 15 268 = 14. However, the reduced strength of the 15 268 Å DIB in HD 147889 rules out a common carrier for these two DIBs. Since the ionisation fraction for small PAHs in this translucent cloud is known to be low compared to diffuse clouds, the weakness of the 15 268 Å DIB suggests that an ionised species could be the carrier of this NIR DIB.