One of the typical error control schemes used in data transmission systems is the selective-repeat ARQ. Previously, the transmission delay for this scheme has been analyzed mostly for an independent error channel. In practice, however, the state of the channel varies with time so that error generation is not independent. This paper considers a non-independent error channel and analyzes transmission delay performance for a selective-repeat ARQ scheme. An error model is used in which the change of the channel state is represented as a 2-state Markov chain. A strict analysis is applied using a discrete-time queuing system and the transmission delay distribution for the frame is derived. When the round-trip propagation delay or the frame queue length is increased, however, a large amount of computation is required in order to obtain the numerical result due to enlargement of the state space. In order to simplify the numerical calculation we give an approximate analysis for the case where the propagation delay or the frame queue length is increased. The average transmission delay is discussed based on numerical examples. As a result, we show that the average transmission delay performance is significantly improved when the decay factor of the Markov chain approaches zero from positive values.