The utility model provides a concentric syntropy friction speed directional well drilling rig includes shell body, turbine stator, turbine rotor, outer axle, the turbine stator is established inside the shell body, and outer epaxial end links to each other with the turbine rotor, and outer axle lower extreme is equipped with outer drill bit and connects, and outer axle is hollow structure, still is equipped with positive displacement motor stator and positive displacement motor rotor in the turbine rotor, and turbine rotor and positive displacement motor stator fixed mounting, positive displacement motor rotor lower part and internal shaft connection, the drill bit connected in interior axle lower extreme was equipped with. This device is installed between bottom hole assembly and drill bit, and it is rotatory to drive two drill bit syntropy friction speeds to it provides optimum rotational speed and moment of torsion parameter to be the broken rock of two drill bits according to technical requirement, it slides to have simultaneously creep into with compound drilling's function, can be applied to the directional well well drilling with the technological advantages of the high -efficient broken rock of two drill bits and be under construction, further improve well drilling efficiency, can also reduce drilling tool transverse vibration, the weight on bit is stabilized to the protection drill bit, improves well trajectory control ability, reduces well drilling comprehensive cost.