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We present a lattice QCD determination of the vector and scalar form factorsof the semileptonic decays D->\pi l \nu and D -> K l \nu which are relevant forthe extraction of the CKM matrix elements |Vcd| and |Vcs| from experimentaldata. Our analysis is based on the gauge configurations produced by theEuropean Twisted Mass Collaboration with Nf = 2+1+1 dynamical fermions. Wesimulated at three different values of the lattice spacing and with pion massesas small as 210 MeV. Our preliminary estimates for the vector form factor atzero 4-momentum transfer are f+(D -> \pi)(0) = 0.610 (23) and f+(D -> K)(0) =0.747 (22), where the uncertainties are only statistical. By combining ourresults with the experimental values of f+(D -> \pi)(0) |Vcd| and f+(D -> K)(0)|Vcs| we obtain |Vcd| = 0.2336 (93) and |Vcs| = 0.975 (30), which together withthe PDG determination of |Vcb| are in agreement with the unitarity constraintof the Standard Model.

D -> \pi l \nu and D -> K l \nu form factors with Nf=2+1+1 Twisted fermions