The band gap bowing parameter of the new semiconductor TlxAl1-xAs alloys are investigated numerically based on first-principles calculations and the local density approximation. A 16-atom supercell is used to model for the ternary TlxAl1-xAs alloys. The alloy's lattice constants obey Vegard's law well. Band gap bowing coefficients show very strong composition dependence. The results suggest that the unstrained band gap bowing parameter of the ternary TlxAl1-xAs alloys is b = 1.9754 eV. The results also suggest that the composition-dependent band gap energy of the zincblende alloys can be expressed by a third-order polynomial equation, E-g(x) = -7.2064x(3) + 14.8397x(2) - 10.016x + 2.2217 eV.