Recently, millimeter-wave (mmWave) communications have received great attention due to the availability of large spectrum resources. Nevertheless, their impact on TCP performance has been overlooked, which is observed that the said TCP performance collapse occurs owing to the significant difference in signal quality between LOS and NLOS links. We propose a novel TCP design for mmWave communications, a mmWave performance enhancing proxy (mmPEP), enabling not only to overcome TCP performance collapse but also exploit the properties of mmWave channels. The base station installs the TCP proxy to operate the two functionalities called Ack management and batch retransmission. Specifically, the proxy sends the said early-Ack to the server not to decrease its sending rate even in the NLOS status. In addition, when a packet-loss is detected, the proxy retransmits not only lost packets but also the certain number of the following packets expected to be lost too. It is verified by ns-3 simulation that compared with benchmark, mmPEP enhances the end-to-end rate and packet delivery ratio by maintaining high sending rate with decreasing the loss recovery time.