A tight-binding-based microscopic theory is developed that accounts for quasilinear conduction bands appearing commonly in transparent conducting oxides. It is found that the interaction between oxygen p and metal s orbtials plays a critical role in determining the band structure around the conduction-band minimum. Under certain types of short-range orders, the tight-binding model universally leads to a dispersion relation which corresponds to that of the massive Dirac particle. The impact of the graphenelike band structure is demonstrated by evaluating the electron mobility of highly doped n-type ZnO.