Algal biomass synthesised nanocomposites have a higher surface area and reusability advantages. This study aimed to synthesise and characterise ZnMgO and silica-supported graphene with ZnMgO (G-ZnMgO) nanocomposites from Kappaphycusalvarezii and evaluate their potential in the application of photocatalysis to remove Rhodamine-B (RhB) and methylene blue (MB) dyes from their aqueous medium by maximising the percentage removal using response surface methodology (RSM) modelling. Nanocomposites were synthesised and characterised by biogenic and instrumental (Powder X-ray diffraction (P-XRD), electron microscopic analysis (SEM and TEM), Fourier transform infrared spectroscopy (FTIR), Energy dispersive analysis of X-rays (EDAX). and UV-visible diffuse reflectance spectroscopy (UV-DRS)) methods, respectively; modelling predicted the optimal conditions to be photocatalyst dosage and contact time of 1 g/L and 90 min, respectively, to obtain maximum MB dye removal of 80% using G-ZnMgO. The results showed the best fit between experimental and RSM predicted values. Thus, the obtained results conclude that the algal biomass synthesised nanocomposites were found to be one of the potential photocatalysts for the removal of RhB and MB dyes from their aqueous solution.