Conventional TCP suffers throughput deadlocks over congested ATM (Asynchronous Transfer Mode) networks due to retransmission timeouts caused by cell loss at ATM level under heavy congestion. A modified congestion control algorithm for TCP is proposed to improve the effective throughput of IP over ATM UBR even in a situation such that an external CBR pressure exist at the same port of the ATM switch. When TCP faces congestion then TCP will reset its retransmission timer. In the proposed algorithm, the MSS (maximum segment size) is reduced from 9140 bytes, the recomended value in RFC 1612, at the same time. When TCP is in fast retransmit machine phase, the MSS is reduced to 512 bytes. A considerable improvement in the effective throughput of TCP has been achieved by these two modifications under relatively small switch buffer size and high CBR stream pressure. The idea, called "Dynamic Granularity Control (DGC)", have been implemented and evaluated on the Linux kernel.