Abstarct: In this work, it is investigated the second harmonic generation of super-Gaussian pulses in an inhomogeneous plasma. Also, the third harmonic generation due to the super Gaussian laser beam with a rippled plasma density is expressed. The process of formulating of the equations in the second and third harmonics is approximately similar to each other. So, considering the electric and magnetic fields and using the Poisson's equation, it is obtained the density of electrons into the plasma. Using the Maxwell's equations, it is obtained the wave equation for the second and third harmonics. Then, it is solved this equation using the 4th order Runge-Kutta method and draw the related graphs. By drawing the diagrams of the changes of the second harmonic field with respect to the change of the laser field amplitude, electron density and refractive index, it can be concluded that the second harmonic field increases with the increase of the parameters of the laser field amplitude, electron density and refractive index. By drawing the graphs of the changes of the third harmonic field with respect to the change of the laser field amplitude, the density of electrons and the refractive index, it is also concluded that by increasing these three parameters, the third harmonic field increases. Moreover, by drawing the graph of the changes of the third harmonic field with respect to the frequency, it can be concluded that the amplitude of the field increases as the frequency decreases.