This paper describes derivation algorithm and evaluation results of a Poincare-Bendixson theorem based target acceleration computation algorithm for autonomous driving on inverse time to collision and time headway plane. Derivation of target acceleration is needed for longitudinal autonomous driving. Ellipsoidal driving area is derived for considering driver’s driving characteristic and safety in time headway-inverse time to collision (TTC) plane. And target acceleration computation algorithm has been proposed based on Poincare-Bendixson theorem. Ellipsoidal driving areas are divided main driving area and real-time driving area. Main driving area is derived based on limit of inverse TTC and time headway for takeover time and human factor, real-time driving area is derived through current driving point with ratio of main driving area. It is designed to computation the target acceleration after deriving the target direction by applying a specific angle based on the normal to the current driving point through the real-time driving area. Specific angle is arbitrary value applied acceleration limitation of actual vehicle. The performance evaluation of target acceleration computation algorithm is has been conducted in Matlab/Simulink environment. It is expected that the proposed algorithm can be used for longitudinal control algorithm for safety and personalization of autonomous vehicle.