Summary: A renewal risk model with constant interest rate was explored. In this model, a delayed claim was induced by every main claim, and the distribution of claim sizes was heavy-tailed. Besides, the fixed premium was changed into a nonnegative stochastic process. And the claim sequences were replaced by extended negatively dependent random variables. An asymptotical expression of the finite time ruin probability was obtained if the claim sizes belong to class \(L \cap D\).