In this letter, we consider the problem of finding sparse signals that share the same support set from their compressed measurements collected at individual sensors in distributed networks, where each sensor has limitations in computational capability and communication power/bandwidth. In order to deal with this problem, we propose a new iterative algorithm which alternates between compressed reconstruction with partially known support at each sensor and adaptive learning support information via cooperative support fusion among sensors. Compared with other existing algorithms, the results obtained by the proposed algorithm show a significant improvement in both noiseless and noisy environments.