Most analytical studies on hybrid automatic repeat request (HARQ) have been carried out in either slow fading or fast fading assumptions. However, since practical wireless channels typically exhibit a time-correlated property, we need to take into account the effects of time correlation in the design of HARQ. In this paper, we analyze the outage probability and delay-limited throughput of HARQ with rate adaptation in a time-correlated channel model. Then, we propose a rate adaptation scheme to maximize the delay-limited throughput and evaluate the performance of the proposed scheme under a delay constraint. Our analytical and numerical results show that the proposed rate adaptation scheme outperforms the conventional rate adaptation schemes. The proposed rate adaptation scheme is further simplified by using a Gaussian approximation on the effective channel power gain. The rate adaptation based on the proposed Gaussian approximation reduces the complexity and achieves a throughput gain comparable to that with the exact channel distributions.