Fourier stability analysis works well and is popular for the finite difference schemes of the linear partial differential equations. However, there are less works on the Fourier convergence analysis, and many of the existing ones require unreasonable assumptions. After removing the assumptions, we provide rigorous Fourier convergence analyses for the equation with one time fractional derivative in our previous work. In the current work, by using different ideas, we propose the rigorous Fourier convergence analyses for the equation with several time fractional derivatives, i.e., the Fokker-Planck equation of tempered fractional LangevinBrownian motion, still without the strong assumptions. The numerical experiments are performed to confirm the theoretical results.