Context. One way to constrain the evolutionary histories of galaxies is to analyse their stellar populations. In the local Universe, our understanding of the stellar population properties of galaxies has traditionally relied on the study of optical absorption and emission-line features. Aims. In order to overcome limitations intrinsic to this wavelength range, such as the age-metallicity degeneracy and the high sensitivity to dust reddening, we must use wavelength ranges beyond the optical. The near-infrared (NIR) offers a possibility to extract information on spectral signatures that are not as obvious in traditional optical bands. Moreover, with the current and forthcoming generation of instrumentation focusing on the NIR, it is mandatory to explore possibilities within this wavelength range for nearby-Universe galaxies. However, although the NIR shows great potential, we are only beginning to understand it. Widely used techniques such as a full spectral fitting and line strength indices need to be tested on systems that are as close to simple stellar populations as possible, and the result from the techniques need to be compared to the yields from a traditional optical analysis. Methods. We present a NIR spectral survey of extragalactic globular clusters (GCs). The set was composed of 21 GCs from the Centaurus A galaxy that were obtained with SOAR/TripleSpec4, which covered the ∼1.0–2.4 μm range with a spectral resolution (R = λ/Δλ) of 3500. These spectra cover Hβ equivalent widths between 0.98 Å and 4.32 Å, and [MgFe]' between 0.24 Å and 3.76 Å. Results. This set was ideal for performing absorption band measurements and a full spectral fitting, and it can be used for kinematic studies and age and abundance measurements. With this library, we expect to be able to probe the capabilities of NIR models, as well as to further improve stellar population estimates for the GCs around the Centaurus A galaxy.