Partial discharge (PD) is the manifestation of insulation degradation, and it is regarded as a great risk in the field of industrial high-voltage insulation system. In this paper, the direction-of-arrival (DOA) estimation algorithm is used for the localization of partial-discharge source. The intersecting point of two rays, which come from two different directions measured by two uniform linear arrays (ULAs), can be regarded as the plane location of partial-discharge source. Fast rise times of partial-discharge pulses result in a wide electromagnetic spectrum, thus this paper focuses on the DOA estimation of wideband signals. The technique of multimodal joint sparse representation (MJSR) has been used to improve the performance of biometrics recognition. Here, we extend it to DOA estimation. The received data are represented by a sparse linear combination of potential steering vectors, while constraining the observations from different frequencies subject to sharing the same sparsity pattern. Based on the simultaneous orthogonal matching pursuit (SOMP) and alternating direction method of multipliers (ADMM), a hard threshold algorithm is proposed for DOA estimation. In order to reduce the computational complexity of hard threshold algorithm, an improved soft threshold DOA estimation algorithm based on the ADMM is proposed as well. The effectiveness of the proposed algorithms is validated by simulations and real tests.