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In this paper adaptive backstepping terminal sliding mode synchronization for a class of uncertain chaotic system is proposed. For finite-time convergence, terminal sliding mode scheme is adopted to backstepping design procedure. It is assumed that only output is measured. Error dynamics is calculated from the difference of output in drive-response system. Finite-time convergent observer is used to estimate unknown state in finite time and designed a control law which made state variables constrained to the terminal sliding surface. States converged to equilibrium in finite time. An appropriate adaptive law is chosen to estimate feedback gain and used Lyapunov theory to verify the stability. We presented a numerical simulation to demonstrate the effectiveness of the proposed method.