Phase locked two laser beams with a tunable and controllable frequency difference in a range of several GHz play a major role in the stimulated Raman transition, coherent population trapping, quantum states preparation and other quantum manipulation researches. We demonstrate such leaser beams with a tunable frequency difference in a range of 6.09.3GHz. In particular, the frequency differences of 6.835GHz and 9.192GHz corresponding to the ground state's hyperfine splitting in Rb87 and Cs133 respectively are realized experimentally. The power of the modulated beam is measured to be 6.87mW. With an antireflection-coated edge-emitting diode placed in an external cavity, we can suppress the carrier completely when the modulation frequency is lower than 4.0GHz by adjusting the external cavity length, the temperature, the current of the diode, and the power of the modulation. When the modulation is higher than 4.0GHz we cannot fully suppress the carrier, but we can also obtain the laser beams each with a high modulation depth due to modulation enhancement by external cavity resonance.