In order to make sure the magnetic field distribution around the magneto-optical trap cold atoms, the weak variation and distribution around the zero-point magnet field can be analyzed. A theoretical analysis is based on the interaction between cold atoms and right-hand circular probe beams. For different transition probability of left and right-hand circularly polarized probe beam before and after zero-point magnetic field, nonlinear magnetic optical rotation (NMOR) induced by cold atoms is computed around the zero-point of 87Rb magneto-optical trap. Using such NMOR effects, rotation angle variation with the magnetic field can be got, even up to an order of magnitude 10-13 T. In the mean time, with such effect a two-peak-dispersionlike structure is developed, which is different from the results mentioned in other papers.