Sparse channel estimation problem is one of challenge technical issues in stable broadband wireless communications. Based on square error criterion (SEC), adaptive sparse channel estimation (ASCE) methods, e.g., zero-attracting least mean square error (ZA-LMS) algorithm and reweighted ZA-LMS (RZA-LMS) algorithm, have been proposed to mitigate noise interferences as well as to exploit the inherent channel sparsity. However, the conventional SEC-ASCE methods are vulnerable to 1) random scaling of input training signal; and 2) imbalance between convergence speed and steady state mean square error (MSE) performance due to fixed step-size of gradient descend method. In this paper, a mixed square/fourth error criterion (SFEC) based improved ASCE methods are proposed to avoid aforementioned shortcomings. Specifically, the improved SFEC-ASCE methods are realized with zero-attracting least mean square/fourth error (ZA-LMS/F) algorithm and reweighted ZA-LMS/F (RZA-LMS/F) algorithm, respectively. Firstly, regularization parameters of the SFEC-ASCE methods are selected by means of Monte-Carlo simulations. Secondly, lower bounds of the SFEC-ASCE methods are derived and analyzed. Finally, simulation results are given to show that the proposed SFEC-ASCE methods achieve better estimation performance than the conventional SEC-ASCE methods. 1