Ruin Probabilities of a risk model with time-correlated claims are studied in this paper. It is assumed that every main claim may produce a by-claim and the occurrence of the by-claim may be delayed. By means of the Laplace tansform, the ruin probabilities of the risk model are obtained. The differential equations of the ruin probabilities are obtained and the explicit expressions of the ruin probabilities are given when the claim sizes are exponentially distributed.