A novel composite based on kappa-Carrageenan (κC) was prepared using N,N-methylene bisacrylamide (MBA) as the crosslinking agent. 5-Hydroxymethylfurfural (5-HMF) was produced by catalytic dehydration of fructose and glucose with MBA grafted κC (κC-g-MBA) as the solid acid catalyst due to sulfonic acid groups in biopolymer skeletons. Various reaction parameters such as optimization of the quantity of the catalyst, temperature, reaction time, and solvent were performed. It was established that for fructose dehydration, the best reaction conditions were the 160 °C as the optimized reaction temperature and 1 h reaction time, respectively. Under these conditions, the HMF yield and fructose conversion were 94.2% and 95.5%, respectively. Furthermore, 160 °C and 2 h were the best reaction temperature and reaction time for glucose dehydration, respectively. Under similar conditions, the HMF yield and glucose conversion are 47% and 93%, respectively. The catalyst was readily prepared from inexpensive materials with considerable reusability and reactivity.