In this paper, the high precision grasping control problem for the Three-joint Aerial Manipulator (TAM) is formulated as a Linear Quadratic Regulator (LQR) problem and a corresponding linear discrete controller is designed. Specially, the deviation of control input at adjacent moments is introduced in the standard quadratic cost function making the control torque change relatively gentle while ensuring the control accuracy. The optimal control input at each moment within finite time is obtained by solving Riccati equation. It is drawn that the designed controller has better convergence and the control torque changes smoother than that of proportional-integral-derivative (PID) controller by simulation experiments.