In this paper, we performed the first-principles calculations of the effects of the uniaxial pressure on electronic structures of the (6, 6) single-walled carbon nanotube crystal (SWNTC). The applied pressure is perpendicular to the axis of carbon nanotubes. The calculated results show that the (6, 6) SWNTC with tetragonal structure (t phase) is metallic, and its electrons can move along the walls of carbon nanotubes. With the increasing of the uniaxial pressure, the (6, 6) SWNTC undergoes the structural phase transitions, and transforms from the t phase to the unbonded phase, and then to the bonded phase. The uniaxial pressure mainly affects the π and π* bands of the band structure of the (6, 6) SWNTC, and these effects on the bands are not only in kxky plane but also in the direction of kz. The electronic properties of the crystal can alter from metal to semiconductor, then to metal again as the uniaxial pressure increases. The distributions of electronic charge densities show that electrons of the unbonded phase are localized near the carbon nanotubes. And electrons of the bonded phase can move not only along the walls of carbon nanotubes, but also between the two nearest nanotubes through the chemical bonds.