Reactor neutrino oscillation experiments, such as Daya Bay, Double Chooz and RENO are designed to determine the neutrino mixing angle θ13 with a sensitivity of 0.01--0.03 in sin2 2θ13 at 90% confidence level, an improvement over the current limit by more than one order of magnitude. The control of systematic uncertainties is critical to achieving the sin2 2θ13 sensitivity goal of these experiments. Antineutrinos emitted from spent nuclear fuel (SNF) would distort the soft part of energy spectrum and may introduce a non-negligible systematic uncertainty. In this article, a detailed calculation of SNF neutrinos is performed taking account of the operation of a typical reactor and the event rate in the detector is obtained. A further estimation shows that the event rate contribution of SNF neutrinos is less than 0.2% relative to the reactor neutrino signals. A global χ2 analysis shows that this uncertainty will degrade the θ13 sensitivity at a negligible level.