Simultaneous adsorption of coexisting organic dyes from industrial wastewater is challenging, and the mechanisms of the coadsorption of these dyes remain unclear. Herein, renewable alginate hybridized with graphene oxide composites were used to investigate adsorption properties of methylene blue (MB) and neutral red (NR) in both single and binary systems. In the monocontaminant system of MB or NR, the adsorption isotherm followed the Langmuir model. Both pseudo-first-order and pseudo-second-order models could well describe the adsorption kinetics of MB and NR. With regards to the adsorption process for both dyes, a diffusion process with two stages was observed. However, in the coadsorption system, competitive adsorption of MB and NR occurred. The adsorption isotherm could be also well described by the Langmuir model, while adsorption kinetics was better fitted by the pseudo-second-order model. Compared to the single system, a one-stage diffusion process occurred in binary systems for both adsorption processes of MB and NR.