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We demonstrate a period poled tapered lithium niobate waveguide and study second harmonic generation (SHG) in this device for the purpose of broadening the quasi-phase matching (QPM) acceptance bandwidth.The finite-difference beam-propagation method is used to simulate the guided modes and calculate the effective indices.The simulation results show that by tapering the width of the cross section linearly,the phase mismatch between a specific input wavelength and its SHG signal can be varied along the propagation length.Ideal SHG phase-matching conditions for a wide range of input wavelengths in communication band firom 1 542.5 nm to 1 553.5 nm can be satisfied in different positions of the waveguide.