In this paper, we extend the Rayleigh-Plesset model by considering the effect of a magnetic field on the nonlinear response of an oscillating spherical air bubble in water. Water molecules in motion, derived by a time varying ultrasound pressure field, suffer a torque from the magnetic field by Lorentz force. The rotational energy and the translational energy together constitute the kinetic energy of the water molecule. The work done by the pressure during the contraction and expansion of bubble is equal to the total kinetic energy of the water molecule in liquid. According to energy conservation, we establish a modified control equation of the bubble motion under the action of an applied external magnetic field. The integration of the nonlinear differential equation governing the bubble motion is performed analytically by using a regular expansion, and is solved numerically by using a fourth-order Runge-Kutta method. It is shown that the variation of ambient pressure changes the bubble dynamics when the magnetic field is off. The ambient pressure is increased due to the effect of external magnetic field. The pressure induced by magnetic field increases linearly with the increase of magnetic field intensity and the coefficient is about 103 times. The bubble expansion rate, maximum radius, and the velocity of the collapsing bubble decrease as the magnetic field increases. It is predicted that the applying of a magnetic field can widen the pressure range and modify bubble dynamics.