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The accuracy of cooperative localization degrades significantly in the non-line-of-sight (NLOS) environments. In addition, the computational complexity of the localization problem often increases dramatically as the scale of a wireless sensor network (WSN) grows. To address these challenges, we propose a distributed NLOS cooperative localization algorithm. First, we propose a new multiplicative model based on the physical mechanism of the NLOS propagation and relax the proposed non-convex model into its convex envelope. This model has a powerful capability to mitigate the NLOS impact and remarkable robustness in changing environments. Second, we design a redundant formulation to decompose the convex problem into numerous sub-problems and then develop an efficient distributed algorithm, which enables each sensor node to locally solve each sub-problem in a parallel way, to decrease the computational complexity. The theoretical analysis and simulations show that the proposed algorithm is superior to the existing methods in both processing speed and localization accuracy.