In this thesis, magnetic _eld decay due to gravitational radiation in neutronrnstar (NS) is theoretically studied. By considering the inuence of therndynamo mechanism"on the generation of a strong magnetic _eld in NS.rnA NS formed as a large star die in a type II supernova, and their magneticrn_elds during formation is 1012 Gauss and 1015 Gauss for both magnetarsrnand pulars, respectively. But their magnetic _eld is decreased. Thus, thisrnstudy focuses on by how much does the magnetic _eld decay using thernmathematical calculation of decay law equation. Based on our _ndings,rnwe have two results. The _rst result shows that, the magnetic _eld of arnrotating NS depends only on the decaying time since the moment of inertiarnis constant. The second result also shows, the magnetic _eld of a rotatingrnNS depends on the decaying time and rotational frequency since momentrnof inertia varies as a function of rotational frequency. The variation inrnmoment of inertia causes to the variation in braking index as a function ofrnrotational frequency. Thus, the quadrapole magnetic _eld is decaying forrnpositive _ and increased for negative _ , respectively.