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 from 1 542.5 nm to 1 553.5 nm can be satisfied in different positions of the waveguide.