Based on the theory of third-order nonlinear Kerr effect in optical fiber, we experimentally demonstrate the generation of photon pairs by exploiting spontaneous four-wave mixing. The photon pairs are produced by pumping a fiber Sagnac loop and a piece of straight fiber with a pulsed laser, respectively. By comparing the experimental results, we analyze how to optimize the experimental parameters to obtain entangled photon pairs with high purity. Our results are useful for developing the all-fiber source of photon pairs and single photon source, which are well suited for quantum communication.