Conventional rotor unmanned aerial vehicles (UAV) mostly adopt the collinear design. It can only generate thrust in the vertical direction, which greatly limits its application in the physical interaction tasks. To solve this problem, this article studies a fully-actuated hexarotor with double-tilted rotors. It can realize independent control of position and attitude by adopting the design method of non-collinear rotor shaft. An improved integral sliding mode ( ISM) controller with chattering suppression is proposed. It is compared with the PID controller, integral backstepping (IB) controller and traditional integral sliding mode controller. Simulation results show that the proposed improved ISM controller can achieve the independent control of the position and attitude of the rotor UAV, which can effectively overcome the uncertainty of its own model parameters and the external wind field disturbance to complete the fixed-point hovering and complex trajectory tracking. Experimental results of the implemented prototype show that the designed fully-actuated rotor UAV can maintain the horizontal attitude during the long-distance lateral motion. The pitch and roll angle errors are controlled within two degrees.