We report the first entanglement swapping experiment using entangled photon-pair sources based on spontaneous four-wave mixing (SFWM). The 1.5-microm band entangled photon pairs generated by SFWM in two independent 500-m dispersion shifted fibers exhibited quantum interference, thanks to the negligible walk-off between the pump and photon pairs. The use of 500-MHz gated-mode InGaAs/InP avalanche photodiodes based on the sine-wave gating technique increased the fourfold coincidence rate. As a result, the formation of an entanglement between photons from independent sources was successfully observed.