Due to small lattice mismatch and large-band-gap difference between SiC and AlN, the light-emitting devices fabricated from (SiC)1-x(AlN)x quaternary semiconductors may be tuned over a wide wavelength range. To understand the feasibility of this application, first-principles calculations have been done to study their electronic structures. It is found that there is a transition of the band gap from indirect to direct when x is greater than about 0.20. The band gap is also found to bow down as a function of x. The calculated results suggest that the direct band gap of (SiC)1-x(AlN)x can be tuned over a wide range from 2.97 to 6.28 eV. Thus, (SiC)1-x(AlN)x is potentially useful for optoelectronic applications.