With more data-driven applications introduced in wide-area monitoring systems (WAMS), data quality of phasor measurement units (PMUs) becomes one of the fundamental requirements for ensuring reliable WAMS applications. This paper proposes a doubly-fed deep learning method for bad data identification in linear state estimation, which can: ① identify bad data under both steady states and contingencies; ② achieve higher accuracy than conventional pre-filtering approaches; ③ reduce iteration burden for linear state estimation; ④ efficiently identify bad data in a parallelizable scheme. The proposed method consists of four key steps: ① preprocessing filter; ② online training of short-term deep neural network; ③ offline training of long-term deep neural network; ④ a decision merger. Through delicate design and comprehensive training, the proposed method can effectively differentiate the bad data from event data without relying on real-time topology information. An IEEE 39-bus system simulated by DSATools TSAT and a provincial electric power system with real PMU data collected are used to verify the proposed method. Multiple test scenarios are applied, which include steady states, three-phase-to-ground faults with (un)successful auto-reclosing, low-frequency oscillation, and low-frequency oscillation with simultaneous three-phase-to-ground faults. The proposed method demonstrates satisfactory performance during both the training session and the testing session.