Electromagnetically induced negative refraction induced by microwave field driving hyperfine level transition is studied by proposing a quasi-lambda type four-level system. Negative refraction characteristics are observed when hyperfine levels within ground state are driven by a microwave field which interacts with electric dipole moment or magnetic dipole moment at different hyperfine levels. In addition, two optical transitions between ground state and excited state are driven by two coupling fields respectively, and the frequency bandwidth of negative refraction is controlled by the detuning of two coupling fields. It is shown that frequency bandwidth of negative refraction is much narrower under off-resonant coupling field than under the resonant coupling field and there is a significant difference in behavior between positively detuned coupling field and negatively detuned coupling field.