We study the dynamic properties of a single semiflexible polymer chain based oil the theory for the wormlike-chain model developed by Hallatschek et al. The linear viscoelastic response is investigated tinder oscillatory forces acting at the two chain ends. The complex compliance and complex modulus are obtained analytically as a function of the oscillation frequency omega. The real part of the complex compliance in the low frequency limit omega -> 0 is consistent with the static result of Marko and Siggia whereas the imaginary part in the low frequency regime exhibits the power-law dependence omega(12). On the other hand, these compliances decrease as omega(-7/8) in the high frequency limit omega -> infinity. This is consistent with the theoretical result obtained by Everaers et al. in a slightly different condition. A scaling argument is developed to get understanding of these novel results.