The present invention provides a fire-resistant steel material superior in HAZ toughness of a welded joint which is high in high temperature yield strength at an envisioned fire temperature of 700 to 800° C. and is free of embrittlement of the welded joint even if exposed at this envisioned fire temperature and a method of production of the same, that is, a fire-resistant steel material of a composition containing, by mass %, C: 0.005% to less than 0.03%, Si: 0.01 to 0.50%, Mn: 0.05 to 0.40%, Cr: 1.50 to 5.00%, V: 0.05 to 0.50%, and N: 0.001 to 0.005% and restricted in contents of Ni, Cu, Mo, B, P, S, and O obtained by heating a steel slab to 1150 to 1300° C., then hot working or hot rolling the slab to an end temperature of 880 degrees or more, acceleratedly cooling the worked or rolled steel material under conditions of a cooling rate at a position of the slowest cooling rate of at least 2° C./sec or more, stopping this accelerated cooling at a temperature region where the surface temperature of the steel material becomes 350 to 600° C., and then allowing the material to cool.