The mechanisms of fatigue crack growth (FCG) in a Ti$_3$Al-based (${alpha}_2$) alloy, Ti-24Al-11Nb (a/o) with acicular microstructure were studied with particular attention focused on the fatigue crack path through the microstructure and on the effects of specimen orientation and crack closure. The results showed that the fatigue cracks of Ti-24Al-11Nb alloy grew much faster than conventional titanium alloys, with little difference in FCG rates for TL and TS orientations. The fatigue crack paths revealed crystallographic transgranular fracture with frequent serrations and branching. This is in agreement with the known effects of slip planarity and microstructure on the FCG behavior. The load-displacement hysteresis loops showed that the crack closure influenced the FCG behavior.