The all fiber sources of photon pairs in the 1550 nm telecom band have the advantages of low cost and compatibility with the fiber network. Further improving the purity will improve the practicality of the quantum light sources. For the pulsed pump field propagating through the optical fiber, a certain amount of chirp will be inevitably induced due to the effects of chromatic of dispersion and Kerr nonlinearity, but its influence on the purity has not been studied yet. In this paper, using photon pairs produced by the spontaneous four wave mixing in dispersion shifted fiber, we study the influence of pump chirp on the purity of photon pairs by varying the chirp of the pulsed pump. For the pump with a given bandwidth, our results demonstrate that the purity of photon pairs having a certain production rate, decreases with the increase of the absolute quantity of pump chirp. Therefore, the purity of the photon pairs with relatively small detuning can be improved by using the transform limited pump pulses due to the suppressed Raman scattering.