The kinematic representation of a rool-pitch seeker was analyzed according to the special structure of the seeker. A geometrical closed-form angle increment solution was proposed based on the Paden-Kahan sub-problems. Using this method, the angle increment solution of the seeker was decomposed into two canonical Paden-Kahan subproblems,which led the solution of inverse kinematics to be two simple rigid motions.Therefore, the complexity of the inverse kinematics problem was reduced. Because the inverse kinematics of the seeker has not an exclusive solution, the minimum angle increment criteria was introduced to optimize the inverse kinematics problem. The numerical simulation shows that the obtained angle inerement allows the pointing error of an optical axis into zero,and the optical axis can be coincident with the line of sight very well. Finally,the semi-physics tracking experiments using the angle increment algrithom for a circle track target were performed,which demonstrates the effectiveness of the proposed inverse kinematics in solving the roll-pitch angle increment.