Accurate channel estimation problem is one of the key technical issues in broadband wireless communications. Standard normalized least mean fourth (NLMF) algorithm was applied to adaptive channel estimation (ACE). Since the channel is often described by sparse channel model, such sparsity could be exploited and then estimation performance could be improved by adaptive sparse channel estimation (ASCE) methods using zero-attracting normalized least mean fourth (ZA-NLMF) algorithm. However, this algorithm cannot exploit channel sparsity efficiently. By virtual of geometrical figures, we explain the reason why ℓ1-norm sparse constraint penalizes channel coefficients uniformly. In this paper, we propose a novel ASCE method using re-weighted zero-attracting NLMF (RZA-NLMF) algorithm. Simulation results show that the proposed ASCE method achieves better estimation performance than the conventional one.