In　this　article,　we　consider　the　numerical　solution　for　the　time　fractional　differential　equations　(TFDEs).　We　propose　a　parallel　in　time　method,　combined　with　a　spectral　collocation　scheme　and　the　finite　difference　scheme　for　the　TFDEs.　The　parallel　in　time　method　follows　the　same　sprit　as　the　domain　decomposition　that　consists　in　breaking　the　domain　of　computation　into　subdomains　and　solving　iteratively　the　sub-problems　over　each　subdomain　in　a　parallel　way.　Concretely,　the　iterative　scheme　falls　in　the　category　of　the　predictor-corrector　scheme,　where　the　predictor　is　solved　by　finite　difference　method　in　a　sequential　way,　while　the　corrector　is　solved　by　computing　the　difference　between　spectral　collocation　and　finite　difference　method　in　a　parallel　way.　The　solution　of　the　iterative　method　converges　to　the　solution　of　the　spectral　method　with　high　accuracy.　Some　numerical　tests　are　performed　to　confirm　the　efficiency　of　the　method　in　three　areas:　(i)　convergence　behaviors　with　respect　to　the　discretization　parameters　are　tested;　(ii)　the　overall　CPU　time　in　parallel　machine　is　compared　with　that　for　solving　the　original　problem　by　spectral　method　in　a　single　processor;　(iii)　for　the　fixed　precision,　while　the　parallel　elements　grow　larger,　the　iteration　number　of　the　parallel　method　always　keep　constant,　which　plays　the　key　role　in　the　efficiency　of　the　time　parallel　method.　©　The　Author(s)　2021.