An effective and reliable Finnis-Sinclair (FS) type potential is developed for large-scale molecular dynamics (MD) simulations of plasticity and phase transition of Magnesium (Mg) single crystals under high-pressure shock loading. The shock-wave profiles exhibit a split elastic-inelastic wave in the [0001]HCP shock orientation and a three-wave structure in the [10-10]HCP and [-12-10]HCP directions, namely, an elastic precursor following the plastic and phase-transition fronts. The shock Hugoniot of the particle velocity (Up) vs. the shock velocity (Us) of Mg single crystals in three shock directions under low shock strength reveals apparent anisotropy, which vanishes with increasing shock strength. For the [0001]HCP shock direction, the amorphization caused by strong atomic strain plays an important role in the phase transition and allows for the phase transition from an isotropic stressed state to the daughter phase. The reorientation in the shock directions [10-10]HCP and [-12-10]HCP, as the primary plasticity deformation, leads to the compressed hexagonal close-packed (HCP) phase and reduces the phase-transition threshold pressure. The phase-transition pathway in the shock direction [0001]HCP includes a preferential contraction strain along the [0001]HCP direction, a tension along [-12-10]HCP direction, an effective contraction and shear along the [10-10]HCP direction. For the [10-10]HCP and [-12-10]HCP shock directions, the phase-transition pathway consists of two steps: a reorientation and the subsequent transition from the reorientation hexagonal close-packed phase (RHCP) to the body-centered cubic (BCC). The orientation relationships between HCP and BCC are (0001)HCP á-12-10ñHCP // {110}BCC á001ñBCC. Due to different slipping directions during the phase transition, three variants of the product phase are observed in the shocked samples, accompanied by three kinds of typical coherent twin-grain boundaries between the variants. The results indicate that the highly concentrated shear stress leads to the crystal lattice instability in the elastic precursor, and the plasticity or the phase transition relaxed the shear stress.