Employing the Poincare index of isolated null-points in a vector field, we worked out a mathematical method of searching for 3D null-points in coronal magnetic fields. After introducing the relevant differential topology, we test the method by using the analytical model of Brown & Priest. The location of null-point identified by our method coincides precisely with the analytical solution. Finally we apply the method to the 3D coronal magnetic fields reconstructed from an observed MDI magnetogram of a super-active region (NOAA 10488). We find that the 3D null-point seems to be a key element in the magnetic topology associated with flare occurrence. Employing the Poincare index of isolated null-points in a vector field, we worked out a mathematical method of searching for 3D null-points in coronal magnetic fields. After introducing the pertinent differential topology, we test the method by using the analytical model of Brown & Priest. The location of null-point identified by our method coincidence precisely with the analytical solution. that the 3D null-point seems to be a key element in the magnetic topology associated with flare occurrence.