We present an experimental realization of a compact and reliable way to build a nondegenerate polarization-entangled photon-pair source based on a dual-periodically-poled $ {\rm Ti}:{{\rm LiNbO}_3} $Ti:LiNbO3 waveguide, which is in the telecommunication window and compatible with the fiber quantum networks. The dual-periodic structure allows two inherently concurrent quasiphase-matching spontaneous parametric down-conversion processes pumped by a single laser beam, hence enabling our source to be compact and stable. We show that our source has a high brightness of $ B = 1.22{\rm } \times {\rm }{10^7}\;{\rm pairs}/(\rm s \times mW \times nm) $B=1.22×107pairs/(s×mW×nm). With quantum state tomography, we estimate an entanglement fidelity of $ 0.945 \pm 0.003 $0.945±0.003. A violation of Clauser-Horne-Shimony-Holt inequality with $ S = 2.75 \pm 0.03 $S=2.75±0.03 is also demonstrated.