Flow around an impulsively rotating square cylinder in a viscous fluid in range of 1 ≤ Re ≤ 300 is numerically investigated by the previously developed LB-DF/FD method, which combines the lattilce Boltzmann method (LBM) and direct-forcing fictitious domain (DF/FD) scheme. Results show that in total three kinds of transient characteristics depending on Re are observed: 1 ≤ Re ≤ 20, four vortices arising from the coers of the square cylinder separate from the surfaces and gradually become stable without vortex integration or shedding; 20 ≤ Re 〈 100, vortices integration is observed when they grow long enough, then separated from each other; Re ≥ 100, vortex shedding takes place in this regime. The shedding vortex joins the downstream vortex to form a new one. It is also found that vortex shedding happens more than one time when Re ≥ 160. Furthermore, each vortex shedding induces a fluctuation in the torque exerted on the cylinder.