Channel estimation problem is one of the key technical issues in time-variant multiple-input multiple-output (MIMO) communication systems. To estimate the MIMO channel, least mean square (LMS) algorithm was applied to adaptive channel estimation (ACE). Since the MIMO channel is often described by sparse channel model, such sparsity can be exploited to improve the estimation performance by adaptive sparse channel estimation (ASCE) methods using sparse LMS algorithms. However, conventional ASCE methods have two main drawbacks: 1) sensitive to random scale of training signal and 2) unstable in low signal-to-noise ratio (SNR) regime. To overcome the two harmful factors, in this paper, we propose a novel ASCE method using normalized LMS (NLMS) algorithm (ASCE-NLMS). In addition, we also proposed an improved ASCE method using normalized least mean fourth (NLMF) algorithm (ASCE-NLMF). Two proposed methods can exploit the channel sparsity effectively. Also, stability of the proposed methods is confirmed by mathematical derivation. Computer simulation results show that the proposed sparse channel estimation methods can achieve better estimation performance than conventional methods.