We　provide　a　parallel　spectral　element　method　for　the　fractional　Lorenz　system　numerically.　The　detailed　construction　and　implementation　of　the　method　are　presented.　Thanks　to　the　spectral　accuracy　of　the　presented　method,　the　storage　requirement　due　to　the　＂global　time　dependence＂　can　be　considerably　relaxed.　Also,　the　parareal　method　combining　spectral　element　method　reduces　the　computing　time　greatly.　Finally,　we　have　tested　the　chaotic　behaviors　of　fractional　Lorenz　system.　Our　numerical　results　are　in　excellent　agreement　with　the　results　from　other　numerical　methods.