We studied the structural and electronic properties of carbon nanotubes under hydrostatic pressures based on molecular dynamics simulations and first principles band structure calculations.It is found that carbon nanotubes experience a hard-to-soft transition as exteal pressure increases.The bulk modulus of soft phase is two orders of magnitude smaller than that of hard phase.The band structure calculations show that band gap of (10,0) nanotube increases with the increase of pressure at low pressures. Above a critical pressure (5.70GPa),band gap of (10,0) nanotube drops rapidly and becomes zero at 6.62GPa. Moreover,the calculated charge density shows that a large pressure can induce an sp2-to-sp3 bonding transition,which is confirmed by recent experiments on deformed carbon nanotubes.