Recently, Dong et al. [Commun. Theor. Phys. 54 (2010) 269-272] proposed two protocols for transmitting unknown quantum states over the collective-dephasing noise channel using Greenberger-Horne-Zeilinger (GHZ) state. This work further extends Dong et al.'s protocols over an insecure channel, in which malicious users attempt to reveal useful information from the transmitted quantum states. Moreover, a secure unknown single-photon transmission protocol will be proposed for collective-rotation noise channel, over which Dong et al.'s work fails to show their non-straight forward constructions.