<p>The fuel plasma in the inertial confinement fusion cycle will be a suitable environment for the formation of disruptive waves and the creation of electromagnetic instabilities. These instabilities prevent symmetrical compression of the target and the formation of a hot spot in the fuel pellet. Filamentation instability is one of the electromagnetic instabilities in the beam-plasma interaction that plays a crucial role in the mechanism of energy transfer from relativistic electrons generated by laser-plasma interaction to the plasma particles of the inertial confinement fusion fuel pellet. Alfvén waves are fundamental waves that refer to low-frequency ion oscillations in the presence of a magnetic field. In this paper, the effect of the Alfvén waves on the growth rate of the filamentation electromagnetic instability has been investigated in the presence of a density gradient and the temperature anisotropy factor in the fuel pellet. To calculate the instability growth rate, kinetic theory based on the Vlasov equation for plasma without magnetic collision is used. The obtained results show that the growth rate of the instability decreases due to the presence of a fuel density gradient and nonlinear wave-wave and wave-particle interactions in the plasma. Additionally, increasing the temperature anisotropy factor leads to an increase in the growth rate and energy loss of the plasma due to the scattering of plasma particles in various directions. Finally, it has been shown that the growth rate of the instability is significantly increased by the presence of background Alfvén waves. This increase in growth rate is due to the increase in energy transfer from plasma ions to electrons in the plasma media, which leads to energy loss and failure to achieve complete burning of the fuel pellets.</p>