Discrete frequency-bin entanglement is an essential resource for applications in quantum information processing. In this Letter, we propose and demonstrate a scheme to generate discrete frequency-bin entanglement with a single piece of periodically poled lithium niobate waveguide in a modified Sagnac interferometer. Correlated two-photon states in both directions of the Sagnac interferometer are generated through cascaded second-order optical nonlinear processes. A relative phase difference between the two states is introduced by changing the polarization state of pump light, thus manipulating the two-photon state at the output of the Sagnac interferometer. The generated two-photon state is sent into a fiber polarization splitter, and then a pure discrete frequency-bin entangled two-photon state is obtained by setting the pump light. The frequency entanglement property is measured by a spatial quantum beating with a visibility of 96.0±6.1%. The density matrix is further obtained with a fidelity of 98.0±3.0% to the ideal state. Our demonstration provides a promising method for the generation of pure discrete frequency-bin entanglement at the telecom band, which is desired in quantum photonics.