Quantum computing and quantum communication, have been greatly developed in recent years and expected to contribute to quantum internet technologies, including cloud quantum computing and unconditionally secure communication. However, long-distance quantum communication is challenging mainly because of optical fiber losses; quantum repeaters are indispensable for fiber-based transmission because unknown quantum states cannot be amplified with certainty. In this study, we demonstrate a versatile entanglement source in the telecom band for fiber-based quantum internet, which has a narrow linewidth of sub-MHz range, entanglement fidelity of more than 95%, and Bell-state generation even with frequency multimode. Furthermore, after a total distribution length of 20-km in fiber, twophoton correlation is observed with an easily identifiable normalized correlation coefficient, despite the limited bandwidth of the wavelength converter. The presented implementation promises an efficient method for entanglement distribution that is compatible with quantum memory and frequency-multiplexed long-distance quantum communication applications.