  We calculated the phase diagram of the Kondo-Heisenberg model on
two-dimensional honeycomb lattice with both nearest-neighbor and
next-nearest-neighbor antiferromagnetic spin exchanges, to investigate the
interplay between RKKY and Kondo interactions at presence of magnetic
frustration. Within a mean-field decoupling technology in slave-fermion
representation, we derived the zero-temperature phase diagram as a function of
Kondo coupling $J_k$ and frustration strength $Q$. The geometrical frustration
can destroy the magnetic order, driving the original antiferromagnetic (AF)
phase to non-magnetic valence bond state (VBS). In addition, we found two
distinct VBS. As $J_k$ is increased, a phase transition from AF to Kondo
paramagnetic (KP) phase occurs, without the intermediate phase coexisting AF
order with Kondo screening found in square lattice systems. In the KP phase,
the enhancement of frustration weakens the Kondo screening effect, resulting in
a phase transition from KP to VBS. We also found a process to recover the AF
order from VBS by increasing $J_k$ in a wide range of frustration strength. Our
work may provide deeper understanding for the phase transitions in
heavy-fermion materials, particularly for those exhibiting triangular
frustration.
