Adsorption and photocatalysis are effective in removing organic pollutants from wastewater. This study is based on the memory effects of MgAl–layered double hydroxides (MgAl–LDHs) after high-temperature calcination. By introducing bismuth vanadate (BiVO4) during the reformation of the layered structure via contact with water, a composite material BiVO4/MgAl–LDHs with enhanced adsorption and visible light catalytic performance was synthesized. The effects of the calcination temperature, ratio, initial methylene blue (MB) concentration, and catalyst dosage on the adsorption and photocatalytic performance were investigated. The BiVO4/MgAl–LDHs showed better photocatalytic performance than the pure BiVO4 and MgAl–LDHs. Under the optimal conditions, the proportion of MB adsorbed in 20 min was 66.1%, and the percentage of MB degraded during 100 min of photolysis was 92.4%. The composite photocatalyst showed good chemical stability and cyclability, and the adsorption-degradation rate was 86% after four cycles. Analyses of the adsorption and photocatalytic mechanisms for the composite material showed that synergistic adsorption and visible light photocatalysis contributed to the excellent catalytic performance of the BiVO4/MgAl–LDHs. A highly adsorbent photocatalytic composite material exhibiting outstanding performance was prepared via a simple, cost-effective, and environmentally friendly method, providing reference information for the removal of organic pollutants from liquids.