Context. Transiting planets offer an excellent opportunity for characterizing the atmospheres of extrasolar planets under very different conditions from those found in our solar system. Aims: We are currently carrying out a ground-based survey to obtain the transmission spectra of several extrasolar planets using the 10 m Gran Telescopio Canarias. In this paper we investigate the extrasolar planet WASP-48b, a hot Jupiter orbiting around an F-type star with a period of 2.14 days. Methods: We obtained long-slit optical spectroscopy of one transit of WASP-48b with the Optical System for Imaging and low-Intermediate-Resolution Integrated Spectroscopy (OSIRIS) spectrograph. We integrated the spectrum of WASP-48 and one reference star in several channels with different wavelength ranges, creating numerous color light curves of the transit. We fit analytic transit curves to the data taking into account the systematic effects present in the time series in an effort to measure the change of the planet-to-star radius ratio (Rp/Rs) across wavelength. The change in transit depth can be compared with atmosphere models to infer the presence of particular atomic or molecular compounds in the atmosphere of WASP-48b. Results: After removing the transit model and systematic trends to the curves we reached precisions between 261 ppm and 455-755 ppm for the white and spectroscopic light curves, respectively. We obtained Rp/Rs uncertainty values between 0.8 × 10-3 and 1.5 × 10-3 for all the curves analyzed in this work. The measured transit depth for the curves made by integrating the wavelength range between 530 nm and 905 nm is in agreement with previous studies. We report a relatively flat transmission spectrum for WASP-48b with no statistical significant detection of atmospheric species, although the theoretical models that fit the data more closely include TiO and VO. The transit light curves are only available at the CDS via anonymous ftp to http://cdsarc.u-strasbg.fr (http://130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/605/A114