Context. The launch of the exoplanet space missions obtaining exquisite photometry from space has resulted in the discovery of thousands of planetary systems with very different physical properties and architectures. Among them, the exoplanet CoRoT-29b was identified in the light curves the mission obtained in summer 2011, and presented an asymmetric transit light curve, which was tentatively explained via the effects of gravity darkening. Aims: Transits of CoRoT-29b are measured with precision photometry, to characterize the reported asymmetry in their transit shape. Methods: Using the OSIRIS spectrograph at the 10-m GTC telescope, we perform spectro-photometric differential observations, which allow us to both calculate a high-accuracy photometric light curve, and a study of the color-dependence of the transit. Results: After careful data analysis, we find that the previously reported asymmetry is not present in either of two transits, observed in July 2014 and July 2015 with high photometric precisions of 300 ppm over 5 min. Due to the relative faintness of the star, we do not reach the precision necessary to perform transmission spectroscopy of its atmosphere, but we see no signs of color-dependency of the transit depth or duration. Conclusions: We conclude that the previously reported asymmetry may have been a time-dependent phenomenon, which did not occur in more recent epochs. Alternatively, instrumental effects in the discovery data may need to be reconsidered. Light curves are only available at the CDS via anonymous ftp to http://cdsarc.u-strasbg.fr (ftp://130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/589/A62