A steerable drilling system , comprising: a rotatable drill string (110; 310; 410; 610) for connecting with a drill bit (140; 640) for drilling a borehole along a drilling trajectory; an active stabilizer (150; 350; 450) comprising: a body (351;451) having an outer surface (352; 452) for contacting a wall of the borehole ; and a plurality of actuators (354; 454) connecting the body (351; 451) and the drill string (110... 610), the plurality of actuators (354; 454) capable of driving the drill string (110...610) to deviate away from a center of the borehole with a displacement to change a drilling direction; a direction parameter measurement module for measuring direction parameters during the drilling, the direction parameters comprising at least one of an inclination angle and an azimuth angle of the borehole; an imbalance parameter measurement module (575; 675) for measuring imbalance parameters during the drilling, the imbalance parameters comprising at least one of a lateral force, a bending moment and a torque at a measuring position near the drill bit; and a controller for controlling the drilling trajectory, the controller comprising a calculator for calculating an adjustment needed for the displacement, characterised in that : the controller is configured to control the drilling trajectory based on the measured direction and imbalance parameters, and the calculator is configured to calculate the adjustment needed for the displacement based on the measured direction and imbalance parameters and expected values of these parameters, wherein the expected values of the direction and imbalance parameters are estimated to compensate a deviation of the drill bit (140; 640) due to the gravity or uneven formation. a rotatable drill string (110; 310; 410; 610) for connecting with a drill bit (140; 640) for drilling a borehole along a drilling trajectory; an active stabilizer (150; 350; 450) comprising: a body (351;451) having an outer surface (352; 452) for contacting a wall of the borehole ; and a plurality of actuators (354; 454) connecting the body (351; 451) and the drill string (110... 610), the plurality of actuators (354; 454) capable of driving the drill string (110...610) to deviate away from a center of the borehole with a displacement to change a drilling direction; a body (351;451) having an outer surface (352; 452) for contacting a wall of the borehole ; and a plurality of actuators (354; 454) connecting the body (351; 451) and the drill string (110... 610), the plurality of actuators (354; 454) capable of driving the drill string (110...610) to deviate away from a center of the borehole with a displacement to change a drilling direction; a direction parameter measurement module for measuring direction parameters during the drilling, the direction parameters comprising at least one of an inclination angle and an azimuth angle of the borehole; an imbalance parameter measurement module (575; 675) for measuring imbalance parameters during the drilling, the imbalance parameters comprising at least one of a lateral force, a bending moment and a torque at a measuring position near the drill bit; and a controller for controlling the drilling trajectory, the controller comprising a calculator for calculating an adjustment needed for the displacement, characterised in that : the controller is configured to control the drilling trajectory based on the measured direction and imbalance parameters, and the calculator is configured to calculate the adjustment needed for the displacement based on the measured direction and imbalance parameters and expected values of these parameters, wherein the expected values of the direction and imbalance parameters are estimated to compensate a deviation of the drill bit (140; 640) due to the gravity or uneven formation. <EOS>