The specific heat of polybutadien was measured and it was found that at temperature Tg = 178K there is a glass transition and the specific heat near the transition temperature depends strongly on the cooling process of the sample. After waiting at temperature Tw for a time tw during the cooling process, we found that there are waiting time effects on the specific heat of a heating process: the anomalous Δcp at Tp increases with the waiting time tw. In thecase of Tw=169K, Δcp(tw) can be described by Kohlrausch law Δcp(tw)～{l-exp[-(tw/τ)β]} with β =0.47±0.03.