The even-even nuclei of Se, Kr, Sr and Zr isotopes are investigated systemically by the constrained relativistic mean field theory with the interactions NL3. The calculated binding energies of ground state for Se, Kr, Sr and Zr isotopes are described fairly well as compared with experiments. By examining the potential energy surfaces obtained by this microscopic approach, it can be found that the shape-coexistence phenomenon is very common in this region. The possible nuclei with shape-coexistence are pointed out systemically and the energy differences between the two minima in the potential energy surfaces for those nuclei are presented as well. In addition, by examining the potential energy surfaces and the microscopic neutron single particle spectra, N=70 are suggested to be a possible neutron magic number in this region.
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