A new two-dimensional structure modulation along c-and b-axes has been discovered in superconducting single crystals of Bi2.13Sr1.87CuO6+δ(Bi2201)by x-ray scattering.Such modulation structure does not exist in non-superconducting Bi2201 single crystals.But instead lattice distortions are observed in the a-b-plane.This phenomenon may indicate that both strain relaxation and charge modulation in the a-b-plane are important to the occurrence of superconductivity in the copper oxides.