In a power system with high proportion of renewable energy, transmission expansion planning (TEP) is further complicated by the intermittency and the volatility of renewable energy, which dramatically increases the diversity of system states. Hence a key problem is that a transmission planning scheme meeting a security criterion under the peak load state may not satisfy the security criterion under other system states. In this paper, to ensure the N-1 security of transmission planning schemes under various system states, a novel robust planning approach considering massive N-1 contingencies is proposed. The convex hull of scenarios is derived by the quick-hull algorithm and then we use the convex combination of vertices to represent any single scenario in the convex hull. Within the adjustable robust optimization framework, the size of the planning model is greatly reduced. A case study implemented on a revised Garver's 6-bus test system shows that the proposed method can ensure the N-1 security criterion of the transmission planning scheme under various system states.