We investigate theoretically the spin states in InAs/AlSb/GaSb broken-gap quantum wells by solving the Kane model and the Poisson equation self-consistently. The spin states in InAs/AlSb/GaSb quantum wells are quite different from those obtained by the single-band Rashba model due to the electron-hole hybridization. The Rashba spin splitting of the lowest conduction subband shows an oscillating behavior. The D'yakonov-Perel' spin-relaxation time shows several peaks with increasing the Fermi wave vector. By inserting an AlSb barrier between the InAs and GaSb layers, the hybridization can be greatly reduced. Consequently, the spin orientation, the spin splitting, and the D'yakonov-Perel' spin-relaxation time can be tuned significantly by changing the thickness of the AlSb barrier.