The band structures of dilute-As AlNAs alloys with As composition ranging from 0% up to 12.5% are studied by using First-Principle Density Functional Theory (DFT) calculation. The energy band gap shows remarkable reduction from 6.19 eV to 3.87 eV with small amount of As content in the AlNAs alloy, which covers the deep ultraviolet (UV) spectral regime. A giant bowing parameter of 30.5 eV ± 0.5 eV for AlNAs alloy is obtained. In addition, our analysis shows that the crossover between crystal field split-off (CH) band and heavy hole (HH) bands occurs in the dilute-As AlNAs alloy with As-content of ~1.5%. This result implies the possibility of dominant transverse electric (TE)-polarized emission by using AlNAs alloy with dilute amount of As-content. Our findings indicate the potential of dilute-As AlNAs alloy as the new active region material for TE-polarized III-Nitride-based deep UV light emitters.