Two types of Ge/Si-based novel tunnel field-effect transistors (TFETs) with source pockets are proposed. In the proposed Ge/Si-based TFETs, the materials in the source, channel, and drain are Ge, Si, and Si, respectively, and the gate shortly overlaps the source. One of the proposed TFETs has an intrinsic Ge pocket and the other has an intrinsic Si pocket, shallowly doped in the source region below the source-overlapped gate. The current-voltage (I-V) characteristics of the proposed Ge/Si-based TFETs were simulated using the TCAD device simulator, and were compared with those of Si, Ge, and Ge (in source)/Si (in channel and drain) TFETs. The on-currents (ION) of the proposed Ge/Si-based TFETs and Ge-TFET were higher, but the subthreshold swing (SS) of the Ge/Si-based TFET with the Ge source pocket was the worst, owing to the hump effect. The off-current (IOFF) of the Ge-based TFET was the worst, but those of the other devices were the same because their drain material was Si, with a larger band gap than Ge. The SS of the proposed Ge/Si-based TFET with a Si source pocket was the best, because the tunneling length of the Ge/Si heterojunction was the shortest, as shown by the simulated energy band. Defect-induce degradation due to large lattice mismatch between Si and Ge materials is investigated including the trap-assisted-tunneling (TAT) model. Overall, the proposed Ge/Si-based TFET with a Si source pocket demonstrated the best performance.