Earth’s intrinsic magnetic field is generated by convection in the outer core. It diverts the continuous plasma flow from the Sun, known as the solar wind, and forms a cavity around Earth called the magnetosphere. The field continually changes its polarity and strength over long timescales, and it is known that the dipole moment has decreased by about 9% over the past 150 years. This decrease is expected to alter the near-Earth environment. In this study, we investigated the development of magnetic storms under the weak intrinsic magnetic field by using global inner magnetospheric simulations. We found that under the weak intrinsic magnetic field, ring current develops faster in the azimuthal direction and the storm intensity is greater compared to the present Earth. Magnetohydrodynamic waves are excited by ring current in all cases. Under the weak intrinsic magnetic field, the amplitude of excited ULF waves was found to be smaller in the dayside and larger in the dawnside.