In recent years, millimeter wave (mmWave) communications, considered as a compelling technology to achieve throughput improvement target of the fifth generation (5G) mobile networks, is quickly attracting attention in both scientific and industrial communities. To enhance reliability of mmWave link, mmWave-LTE networks with MPTCP could be used as an effective solution due to its path diversity. However, the poor performance of MPTCP is found in mmWave-LTE networks based on previous studies. In this paper, we identify the reason of the preceding problem which is the congestion window overgrowth in Slow Start phase, and propose a BDP Estimation Based Slow Start (BESS) algorithm for MPTCP to address this problem. Our simulations show that with the control of BESS, MPTCP can sufficiently use the bandwidth of mmWave networks, and improve networks robustness when mmWave link is switched from LOS to NLOS condition.