Aims: As a sub-Uranus-mass low-density planet, GJ 3470b has been found to show a flat featureless transmission spectrum in the infrared and a tentative Rayleigh scattering slope in the optical. We conducted an optical transmission spectroscopy project to assess the impacts of stellar activity and to determine whether or not GJ 3470b hosts a hydrogen-rich gas envelop. Methods: We observed three transits with the low-resolution Optical System for Imaging and low-Intermediate-Resolution Integrated Spectroscopy (OSIRIS) at the 10.4 m Gran Telescopio Canarias, and one transit with the high-resolution Ultraviolet and Visual Echelle Spectrograph (UVES) at the 8.2 m Very Large Telescope. Results: From the high-resolution data, we find that the difference of the Ca ii H+K lines in- and out-of-transit is only 0.67 ± 0.22%, and determine a magnetic filling factor of about 10-15%. From the low-resolution data, we present the first optical transmission spectrum in the 435-755 nm band, which shows a slope consistent with Rayleigh scattering. Conclusions: After exploring the potential impacts of stellar activity in our observations, we confirm that Rayleigh scattering in an extended hydrogen-helium atmosphere is currently the best explanation. Further high-precision observations that simultaneously cover optical and infrared bands are required to answer whether or not clouds and hazes exist at high-altitude. Based on observations made with the Gran Telescopio Canarias (GTC), at the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrofísica de Canarias, on the island of La Palma, as well as observations obtained at the European Southern Observatory at Paranal, Chile in program 096.C-0258(A).