hot-rolling a cast slab as cast or cooled once,

said cast slab containing, in terms of weight %,

C: 0.02 to 0.3%,

at least one or more element selected from the group consisting of, total 0.1 to 3.5%, in terms of weight %,

Mn: 0.05 to 3%,

Ni: 3% or less

Cr: 3% or less,

Cu: 3% or less,

Mo: 1% or less,

Co: 3% or less and

Sn: 0.2% or less,

Si: 3% or less and

Al: 3% or less

then reheated to a range of 1000 to 1300° C., with a total reduction ratios of 25% or more at Ar₃ to (Ar₃₊150)° C., temperature at finishing hot-rolling start, TFS, and temperature at finishing hot-rolling end, TFE, and calculated residual strain Δε to simultaneously satisfy following relations (1) to (4), and

cooling hot-rolled steel sheet, then

coiling at below critical temperature T₀ determined by the chemical composition of the steel shown in the following relation (5) and a temperature of not more than 400° C.:

TFE≧Ar₃ (° C.)  (1)

TFS≤1100° C.  (2)

Δε≧(TFS−TFE)/375  (3)

20° C.≤(TFS−TFE)≤120° C.  (4)

T₀=−650.4×{C %/(1.82×C %−0.001)}+B  (5)

where, B is found from the composition of the steel expressed by weight %,

Δε is found from the equivalent strain εi (i is 1 to n) given at each stand of the n stages of finishing rolling for the rolling, time ti (sec) (i=1 to n−1) between stands, time tn (sec) from the final stand to the start of cooling, rolling temperature Ti(K) (i=1 to n) at each stand, and a constant R=1.987,

ε=Δε1+Δε2+ . . . +Δεn

where, Δεi=εi ×exp{−(ti*/τn)^2/3}

τn=8.46×10⁻⁹×exp{43800/R/Ti}

ti*=τn×(ti/τi+t (i+1)/τ(i+1)+ . . . +tn/τn}.