The discrete single-particle spectra in both the Fermi and Dirac sea have been calculated by the imaginary time step (ITS) method for the Schrödinger-like equation after avoiding the "tsunami" of the Dirac sea, i.e. the diving behavior of the single-particle level into the Dirac sea in the direct application of the ITS method for the Dirac equation. It is found that by the transform from the Dirac equation to the Schrödinger-like equation, the single-particle spectra, which extend from the positive to the negative infinity, can be separately obtained by the ITS evolution in either the Fermi sea or the Dirac sea. Identical results with those in the conventional shooting method have been obtained via the ITS evolution for the equivalent Schrödinger-like equation, which demonstrates the feasibility, practicality and reliability of the present algorithm and dispels the doubts on the ITS method in the relativistic system.