We study the central (inner few hundred parsecs) stellar populations of four starburst galaxies (NGC 34, 1614, 3310 and 7714) in the near-infrared (NIR), from 0.8 to 2.4 μm, by fitting combinations of stellar population models of various ages and metallicities. The NIR spectra of these galaxies feature many absorption lines. For the first time, we fit simultaneously as much as 15 absorption features in the NIR. The observed spectra are best explained by stellar populations containing a sizable amount (20–56 per cent by mass) of ∼1-Gyr-old stellar population with thermally pulsing asymptotic giant branch stars. We found that the metallicity of the stars which dominates the light is solar. Metallicities substantially different from solar give a worse fit. Though the ages and metallicities we estimate using the NIR spectroscopy are in agreement with values from the literature based on the ultraviolet/optical, we find older ages and a larger age spread. This may be due to the fact that the optical is mostly sensitive to the last episode of star formation, while the NIR better maintains the record of previous stellar generations. Another interesting result is that the reddening estimated from the whole NIR spectrum is considerably lower than that based on emission lines. Finally, we find a good agreement of the free emission-line spectrum with photoionization models, using as input spectral energy distribution the synthetic composite template we derived as best fit.