A combined input and crosspoint queued (CICQ) switch with a flow control latency of round-trip time (RTT) packets requires each crosspoint (CP) buffer to hold the RTT packets in order to support any traffic pattern without blocking. In this paper, a distributed rate-based flow control internal to a CICQ switch is proposed. The new rate-based flow control allocates bandwidth to each virtual output queue (VOQ) using simple counters, and a minimal CP buffer requirement can be achieved without packet loss. The proposed rate-based flow control is shown to be more stable than the existing credit-based flow control previously proposed in the literature for realistic traffic while significantly reducing the CP memory size, thus making the implementation of a distributed CICQ switch practical.