Observations have shown that there exists downward propagation of alternating westward/eastward jets in Jupiter’s equatorial stratosphere, with a quasi-period between 4 and 6 yr. This phenomenon is generally called the quasi-quadrennial oscillation (QQO). Here, we simulate the QQO by injecting isotropic small-scale thermal disturbances into a 3D general circulation model of Jupiter. It is found that the internal thermal disturbance is able to excite a wealth of waves that generate the equatorial QQO and multiple jet streams at the middle and high latitudes of both hemispheres. The dominant wave mode in generating the QQO-like oscillation is that with a zonal wavenumber of 10. The inhomogeneous evolution of potential vorticity favors the emergence of off-equatorial zonal jets. The off-equatorial jets migrate to the equator, strengthen the deep equatorial jets, and result in the prolonging of the QQO-like oscillations.