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As large-scale wind farms (WFs) are integrated with the power grid, the interaction between the WF and the grid may excite torsional vibration of the shaft of the wind turbine. To study the shaft's torsional vibration characteristics of a doubly fed induction generator (DFIG)-based WF, a detailed small-signal model of DFIG is established first. Then the small-signal model for a WF composed of multiple DFIGs is developed on the basis of the single-machine model. Modal analysis is employed to investigate the torsional vibration characteristics of a WF made up of several identical DFIGs, whose accuracy is also demonstrated through time-domain simulation. To simplify the torsional vibration analysis for the DFIG-based WF, a reduced-order equivalent model is proposed. The results obtained from modal analysis show that the equivalent model not only precisely maintains all the torsional vibration modes of the original small-signal model but also greatly reduces the computation complexity. With the equivalent model, the 'curse of dimensionality' problem is solved in torsional vibration analysis for large WFs, which is of great help in the design of further damping schemes.