In　this　paper,　we　propose　two　numerical　methods　for　solving　certain　kinds　of　mean-field　backward　stochastic　differential　equations:　first-order　numerical　scheme　and　Crank-Nicolson　numerical　scheme.　Then,　we　study　L-p-error　estimates　for　the　proposed　schemes.　We　prove　that　the　two　schemes　are　of　second-order　convergence　in　solving　for　Y-t　in　L-p　norm;　the　first-order　scheme　is　of　first-order　convergence　and　the　Crank-Nicolson　scheme　is　of　second-order　convergence　in　solving　Z(t)　in　L-p　norm.