A steel sheet undergone precipitation strengthening and refinement in crystal grain size by containing at least one element of 0.005% to 0.05% of Nb, 0.005% to 0.05% of Ti, and 0.0005% to 0.005% of B as a chemical composition is produced through continuous annealing. A steel containing at least one element of Nb, Ti, and B is hot rolled, cooled at a cooling rate of 40° C./s or less, and coiled at 550° C. or higher to facilitate precipitation of cementite after recrystallization annealing. As a result, a steel sheet for a can having a tensile strength of 450 to 550 MPa, a total elongation of 20% or more, and a yield elongation of 5% or less is produced.