A robust sparse least-mean mixture-norm (LMMN) algorithm is proposed, and its performance is appraised in the context of estimating a broadband multi-path wireless channel. The proposed algorithm is implemented via integrating a correntropy-induced metric (CIM) penalty into the conventional LMMN algorithm to modify the basic cost function, which is denoted as the CIM-based LMMN (CIM-LMMN) algorithm. The proposed CIM-LMMN algorithm is derived in detail within the kernel framework. The updating equation of CIM-LMMN can provide a zero attractor to attract the non-dominant channel coefficients to zeros, and it also gives a tradeoff between the sparsity and the estimation misalignment. Moreover, the channel estimation behavior is investigated over a broadband sparse multi-path wireless channel, and the simulation results are compared with the least mean square/fourth (LMS/F), least mean square (LMS), least mean fourth (LMF) and the recently-developed sparse channel estimation algorithms. The channel estimation performance obtained from the designated sparse channel estimation demonstrates that the CIM-LMMN algorithm outperforms the recently-developed sparse LMMN algorithms and the relevant sparse channel estimation algorithms. From the results, we can see that our CIM-LMMN algorithm is robust and is superior to these mentioned algorithms in terms of both the convergence speed rate and the channel estimation misalignment for estimating a sparse channel.