Optical gain characteristics of $1.3{mu}m$ type-II GaAsSb/InGaNAs/GaAs trilayer quantum well structures were studied using multi-band effective mass theory. The results were compared with those of $1.3{mu}m$ GaAsSb/InGaNAs/GaAs trilayer quantum well structures. In the case of $1.3{mu}m$ GaAsSb/InGaNAs/GaAs trilayer quantum well structure, the energy difference between the first two subbands in the valence band is smaller than that of $1.3{mu}m$ GaAsSb/InGaNAs/GaAs trilayer quantum well structure. Also, $1.3{mu}m$ GaAsSb/InGaNAs/GaAs trilayer quantum well structure shows larger optical gain than $1.3{mu}m$ GaAsSb/InGaNAs/GaAs trilayer quantum well structure. This means that GaAsSb/InGaNAs/GaAs system is promising as long-wavelength optoelectronic devices for optical communication.