Combining a Ti-diffusion periodically poled lithium niobate (PPLN) waveguide with a Sagnac interferometer, two opposite directions type-II spontaneous parametric down conversions (SPDC) occur coherently and yield a high brightness, high stability polarization entanglement source. The source produces degenerate photon pairs at 1540.4 nm with a brightness of B = (1.36 ± 0.03) × 106 pairs/(s⋅nm⋅mW). We perform quantum state tomography to reconstruct the density matrix of the output state and obtain a fidelity of F = 0.983 ± 0.001. The high brightness and phase stability of our waveguide source enable a wide range of quantum information experiments operating at a low pump power as well as hold the advantage in mass production which can promote the practical applications of quantum technologies.