The design of stimuli-responsive drug carrier for controlled drug release is of significant importance in pharmaceutics, medicine and biology. Here, sodium alginate (SA) was integrated with graphene oxide (GO) by using Ca2+ as the crosslinker. The resultant SA-Ca2+-GO composites were freeze-dried to produce SA-Ca2+-GO hybrids, which were then examined by Fourier transform infrared (FT-IR) spectrometry, field emission scanning electron microscopy (FESEM) and atomic force microscopy (AFM). The SA-Ca2+-GO hybrids were used as the drug carrier of methotrexate (MTX), and electro- and pH-responsive release of MTX was successfully achieved due to the excellent conductive ability of GO and the pH-sensitive property of SA. Finally, Higuchi model was employed to investigate the release kinetics of MTX from the SA-Ca2+-GO hybrids, and the results indicate that the release of MTX is controlled by Fickian diffusion.