An anti-blast concrete and a method of fabricating an anti-blast structure member using such anti-blast concrete are disclosed. The composition of the anti-blast concrete according to the invention includes, in parts by weight, 1.0 part by weight of cement, 1.0 to 2.5 parts by weight of fine aggregates, 1.0 to 2.5 parts by weight of coarse aggregates, and a plurality of reinforcing fibers. The weight ratio of the reinforcing fibers to the cement ranges from 0.5% to 3%. The plurality of reinforcing fibers are a plurality of carbon fibers or a plurality of aramid fibers. A test body, made of the anti-blast concrete of the invention, has an average number of times of repeated impacts at an impact energy of 49.0 Joules equal to or larger than 41 times at 28 days of age.