This paper describes design of a back-channel feedback corpus and its evaluation, aiming at realizing in-car spoken dialogue systems with the high responsiveness. We constructed our corpus by annotating the existing in-car spoken dialogue data with back-channel feedback timings in an off-line environment. Our corpus is practically available in developing dialogue systems which can provide the back-channel feedbacks. As an evaluation result, we confirmed that our proposed design enabled the construction of the back-channel feedback corpus with high coherency and naturalness.