The split Hopkinson tensile bar (SHTB) tests are carried out for three structural steels, i.e., Q355 steel, Q460 steel and Q620 steel, for the increasing demand on the mechanical properties of steels at high strain rates. Four strain rate levels, i.e., 1000 s−1, 2000 s−1, 3000 s−1 and 4000 s−1, are used in the tests. The corresponding quasi-static tensile loading tests are also performed for comparison. The observation of fracture morphology and the metallographic organization is also conducted to reveal the mechanism of steel under high strain rate loading. Subsequently, a stress–strain relationship model is proposed based on the modified Johnson–Cook model, and the parameters are calibrated by data from both quasi-static tensile tests and SHTB tests. The results show that the effect of strain rate hardening on the strength of steel is significant, and the proposed model can well describe the mechanical behaviour of these three structural steels at high strain rates.