The Weibel instability is one of the basic beam-plasma electromagnetic instabilities which dependents to the plasma particle distribution function. The beam-plasma particle distribution function plays an important role in the energy traveling mechanism of relativistic electrons generated by the laser-plasma interaction in the Inertial Confinement Fusion Plasma. In this paper, an analytical expression of the beam-plasma particles distribution function effect such as; the Kappa, Semi-relativistic Maxwellian and Maxwell distributions on the Weibel electromagnetic instability growth rate is investigated in strongly coupled plasmas under the low-frequency wave condition. The obtained results show that the maximum instability growth rate of the plasma particles with Kappa distribution function is based on the temperature anisotropy parameter, density gradient, quantum parameter and relativistic parameter have the highest possible value compared to the other two plasma particles distribution functions. Also, the Maxwellian distribution function has a more stable growth rate than the Kappa and the Semi-relativistic distribution functions.
