The combined drive current of the lower hybrid wave (LHW) and the high harmonic fast wave (HHFW) is studied for the first time, based on the use of low and higher β_e operational parameters in EAST. Broad and significant synergistic effects are found in the simulation, the local synergy factor reaching a factor of 4.3 in the off-axis region. The current drive (CD) efficiency is greatly improved, and the current profile is modified as a result of the synergy between the two types of waves . the LHW interacted with the resonant electrons in low parallel velocity region and pushes them into the adjacent resonance region of the high phase velocity wave (HHFW), the number of fast electrons resonant with the HHFW is increased dramatically, and the driven current is enhanced. Therefore the synergy effect strongly depends on the positional relational between the velocity resonance regions of the two waves. Moreover, the effects of the parallel refractive index and the wave power on the synergy effect are examined. Some problems well known in the single LHW CD or the HHFW CD may be overcome by the combined CD.