Abstract: This paper investigates a dependent heavy-tailed risk model with constant interest rate, where the claim sizes are a sequence of upper extended negatively dependent random variables; the claim arrival process is a general nonnegative integer-valued counting process, which is independent of the claim sizes; and the premium process is a general nonnegative and nondecreasing stochastic process. We obtain an asymptotic result on the finite-time ruin probability of an insurance company in two cases, where, one is the claim sizes, the claim arrival process and the premium process are mutually independent; the other is the tail probability of the total discounted amount of premiums can be highly dominated by that of the claim size. Besides, we conduct some numerical simulations to verify the accuracy of the asymptotic relation in the obtained result.