We demonstrate a stable source of high quality telecom-band polarization-entangled photon-pairs based on a single, pulse-pumped, short periodically-poled lithium niobate (PPLN) waveguide. Full quantum state tomographic measurement performed on the photon-pairs has revealed a very high state purity of 0.94, and an entanglement fidelity exceeding 0.96 at the low-rate-regime. At higher rates, entanglement quality degrades due to emission of multiple-pairs. Using a new model, we have confirmed that the observed degradation is largely due to double- and triple-pair emissions.