Coherent terahertz (THz) emission from the vacuum-plasma interface induced through laser wake-field excitation has been investigated by particle-in-cell simulations. The emission frequency appears around tau(-1)(L), where tau(L) is the laser pulse duration, even though the plasma density is distributed inhomogeneously near the interface. The emission amplitude, which is zero on the propagation axis of the incident pulse, increases transversely until reaching the maximum amplitude at the beam edge of the incident pulse and then decays transversely. The emission power scales like P approximately 10(8) x a(4)(0) W, where a(0) is the normalized field amplitude of the laser pulse. For an incident pulse of a few tens of femtoseconds at the forced intensity of 3 x 10(17) W/cm(2), it can generate THz radiation with a power of a few MW and with an energy of several microJ/pulse.