The deformation and fracture behaviors, in tension and in compression, of a TiAl-V alloy with polysynthetically twinned(PST) structure have been studied. It has been found that the room temperature ductilities in tension and in compression are quite different and this difference is closely related to the crack propagating way. When loading axis is perpendicular to the lamellar boundary (-90°), fracture stain is almost zero in tension while it is the largest one in compression. When the angle W between loading axis and the lamellar boundary decreases, fracture strain increases in tension but decreases in compression. When =90°, cracks tend to propagate along lamellar boundaries in tension while they tend to propagate across lamellar boundaries in compression. However, when =0°, cracks tend to propagate across the lamellar boundary in tension while they tend to propagate along the lamellar boundary in compression. The influence of crack propagating way and resolved normal stress component of extra stress on the ductility has been discussed.