In high-speed packet networks, protocol processing overhead time becomes remarkable in determining the system performance. In this paper, we present a new Selective-Repeat ARQ scheme (called Block SR-ARQ sheme), in which a packet is transmitted or retransmitted in the same way as basic SR-ARQ scheme, but a single acknowledgement packet is used to acknowledge a block of packets. The maximum number of packets acknowledged by an acknowledgement packet is defined as block size. We analyze the system throughput and the average packet delay over the system, and the accuracy of approximately analyzed results is validated by simulation. Furthermore, we show that there exists an optimal block size which obtains both the maximum throughput and the minimum average packet delay.