Abstract: The effects of magnetic field on the nucleon in finite isospin chemical potential are discussed in the framework of Skyrme model. Based on the criterion that there is a unique stable solution below the critical value of isospin chemical potential, while multiple unstable solutions above this value, the critical values at various magnetic fields can be identified accurately. It is found that the critical value of isospin chemical potential enlarges with increasing magnetic field which indicates that the magnetic field can reduce the instability of a nucleon induced by isospin chemical potential. The critical values of a neutron are greater than those of a proton for cases where the magnetic field is not equal to zero. It implies that in the presence of magnetic field the neutron can be stable at more isospin-asymmetric nuclear matter than the proton. The magnetic field can significantly increase the radius, mass and magnetic moment of a nucleon when the isospin chemical potential approaches the critical value.