In order to design a fast-convergence, low steady-state error and robust adaptive filtering algorithm, based on the diffuse LMS algorithm, a distributed adaptive network filtering algorithm based on the unknown parameter estimation constraint is proposed. In the proposed method, during the iterative convergence process, the step size is adaptively adjusted according to the difference norm of parameter estimates between adjacent iterations. Thus, a large step size is used to accelerate the convergence at a faster speed in the initial estimation period, and an adaptive adjustment step length is used in the later period to maintain a relatively low steady-state error. Comparison of experimental results shows that, the proposed algorithm performs better in distributed estimation comparing with ATC-DSELMS, ATC-DLMS and ATC-DLMS/F algorithms.