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The problem of global finite-time convergent observer design for a class of nonlinear systems with time-varying coefficients is investigated in this paper. To solve this problem, a new time-varying finite-time convergent observer is first designed for the nominal system without nonlinearities. Using a recursive argument, an explicitly homogeneous Lyapunov function is constructed to prove the finite-time convergence of the error dynamic system. Then, using the homogeneous domination approach, we scale the finite-time observer with an appropriate choice of gain to obtain a global finite-time convergent observer for the nonlinear system.