We studied theoretically excitons in narrow-coupled InAs/GaSb quantum wells where there is not any overlap between the InAs conduction subband and the GaSb valence subband. In this case, excitons do not exist in the equilibrium and the luminescence of pumped excitons can be observed. We calculated the exciton binding energy making use of the variational method. The resulting binding energy is around 4 meV. We also calculated the exciton lifetime for both radiative recombination and nonradiative recombination. Due to the unique band alignment of InAs/GaSb, the recombination can happen via two channels: first, mixing of the conduction band of InAs with the valence band of GaSb and second, electron tunneling from InAs conduction band to GaSb conduction band and hole tunneling from GaSb valence band to InAs valence band. The fastest recombination process is the radiative process in the second channel. The lifetime varies with the well widths from 45 ps for narrow wells to 400 ps for wider wells.