We investigate the phase transitions in InAs/GaSb quantum wells sandwiched between two wide-gap AlSb barrier layers under an external electric field perpendicular to interfaces. The Schrödinger and the Poisson equations are solved self-consistently to derive the subband dispersions, the potential profile, the electron charge distribution in the InAs layer, and the hole charge distribution in the GaSb layer. The Burt-Foreman envelope function theory and the scattering matrix method are used to solve the Schrödinger equation in the framework of the eight-band k · p model, including the spin-splitting of subbands in our calculation. We have found that in a thick InAs/GaSb quantum well, which has been investigated experimentally by Cooper et al (1998 Phys. Rev. B 57 11915), under low external electric fields, two electron levels stay below the highest hole level at zero in-plane wavevector k ∥ = 0. Then, the anticrossings of electron and hole levels produce several minigaps in the in-plane dispersions, inside which the states of other subbands exist. As a result, the system is in a semimetal phase. With increasing external electric field, the semimetal phase changes to semiconductor phase with only one hybridization gap. When all electron levels become higher than the hole levels at higher electric fields, the system has a semiconducting gap.