  We calculate the vacuum fluctuation of the stress tensor of a
higher-derivative theory around a thin cosmic string. To this end, we adopt the
method to obtain the stress tensor from the effective action developed by
Gibbons et al. By their method, the quantum stress tensor of higher-derivative
scalar theories without self-interaction is expressed as a simple sum of
quantum stress tensors of free massive scalar fields. Unlike the vacuum
expectation value of the scalar field squared obtained in the similar model,
there appears no reduction of the values near the conical singularity.
