TCP-based applications account for a majority of data traffic in the Internet; thus, understanding and improving the performance of TCP over optical burst switching (OBS) network is critical. In this paper, we identify the ill effects of implementing TCP over a hybrid network (IP-access and OBS-core). We propose a Split-TCP framework for the hybrid IP-OBS network to improve TCP performance. We propose two Split-TCP approaches, namely, 1:1:1 and N:1:N. We evaluate the performance of the proposed approaches over an IP-OBS hybrid network. Based on the simulation results, N:1:N Split-TCP approach outperforms all other approaches. We also develop an analytical model for end-to-end Split-TCP throughput and verify it with simulations.