Recently, Park and Lim (1998) proposed two key distribution systems for secure VSAT satellite communications. One provides indirect authentication, and another scheme enables that two parties can directly authenticate each other. However, this article will show that the proposed schemes are insecure enough by presenting two impersonation attacks on them. Besides, an improved scheme will be proposed, which is secure against the impersonation attack and provides direct mutual authentication between two parties. Key words: satellite communication, key distribution, cryptanalysis.