We investigate the structural and dynamical properties of the DX center in Si-doped GaAs under pressure through self-consistent ab initio pseudopotential calculations. The negatively charged broken-bond configuration for the DX center is found to be the ground state against the shallow-donor level at pressures above 24 kbar, in good agreement with measured values. This configuration is also found to be more stable than a tetrahedrally symmetric breathing-mode distortion of the donor neighboring atoms, which induces a localized level. The calculated local vibrational frequencies for both the shallow donors and deep DX centers are generally underestimated compared with experimental results, while their pressure dependences are in good agreement with experiments. However, the pressure coefficient of the donor vibrating mode in the breathing-mode distortion is found to be about twice as large as measured values.