To provide a steel sheet excelling in mechanical strength, processability and thermal stability that is suitable as a material for use in automobiles, home electric appliances, mechanical structures, architecture, etc. and provide a process for producing the same. There is provided a steel sheet of low-alloy steel or carbon steel whose main phase consists of ferrite, wherein the average crystal grain diameter of ferrite at a position of depth corresponding to 1/4 of the sheet thickness from the steel sheet surface, D mum, satisfies the following formulae (1) and (2), and wherein the rate of increase at 700 DEG C of average crystal grain diameter of ferrite at a position of depth corresponding to 1/4 of the sheet thickness from the steel sheet surface, X [mu]m/min, and the above average crystal grain diameter D satisfy the following formula (3). 1.2<=D<=7 (1) D<=2.7+5000/(5+350C+40Mn)<2> (2), DX<= 0.1 (3).