A concrete composition from waste ascon is provided, which shows 150kgf/cm2 or more of early strength in 10 to 20 minutes under laying process of urgent construction. A highly fast cured concrete composition comprises: 50%±5% by weight of highly fast cured cement comprising 50% to 79.9% by weight of 3CaO.3Al2O3.CaSO4 in the form of solid powder of 6,000cm^2/g to 12,000cm^2/g; 15% to 25% by weight of gypsum anhydrite in the form of solid powder of 6,000cm^2/g to 12,000cm^2/g; 5% to 30% by weight of Portland cement; and 0.1% to 3.0% of super-plasticizer, blended as 100 parts by weight in total. Additionally, the composition comprises 0.00001% to 0.3% of retardant depending on the outside temperature. The highly fast cured concrete composition is prepared by blending 50%±5% by weight of the prepared concrete composition with 50%±5% by weight of waste ascon ground in the form of particles of 5mm to 0.1mm in 10% to 12% by weight of blending water with respect to 100 parts by weight of used cement. The ratio of waste ascon and aggregates is 50%±5%:50%±5% with respect to 100 parts by weight of the ascon of 50%±5% by weight. The blending water is prepared by blending 20% to 25% of aqueous polymer emulsion having 40% to 50% of solid contents with 75% to 80% of water for 100 parts by weight.