Generalized projective synchronization of chaotic systems is a new type of chaos synchronization, which has many applications in areas like secure communication, cryptosystems and data encryption. In this paper, we have derived new results on the adaptive controller design for the generalized projective synchronization (GPS) of identical Elhadj chaotic systems (2008) with unknown system parameters. Lyapunov stability theory and adaptive control theory have been applied for deriving the new GPS results for Elhadj systems with unknown system parameters. MATLAB plots have been depicted to demonstrate the adaptive GPS results obtained for the Elhadj chaotic systems.