In this paper, we propose a new diffusion sparse equal-scale adaptive RLS algorithm for distributed learning problem in the diffusion network. This algorithm makes two improvements to the traditional diffusion RLS algorithm. One is adding a sparse perception factor to the cost function of the RLS algorithm, which makes it perform better when identifying sparse systems. The second, we use an adaptive coefficient in the iterative equation, this improvement can speed the convergence rate of the algorithm. Meanwhile, the theoretical analysis shows the proposed algorithm has the first-order and second-order convergence rate. A simulation is given and it shows that the algorithm is better than the compared existing algorithms in terms of convergence rate and steady-state super mean square error.