This paper describes a new semi-blind source separation (semi-BSS) technique with independent component analysis (ICA) for enhancing a target source of interest and for suppressing other known interference sources. The semi-BSS technique is necessary for double-talk free robot audition systems in order to utilize known sound source signals such as self speech, music, or TV-sound, through a line-in or ubiquitous network. Unlike the conventional semi-BSS with ICA, we use the time-frequency domain convolution model to describe the reflection of the sound and a new mixing process of sounds for ICA. In other words, we consider that reflected sounds during some delay time are different from the original. ICA then separates the reflections as other interference sources. The model enables us to eliminate the frame size limitations of the frequency-domain ICA, and ICA can separate the known sources under a highly reverberative environment. Experimental results show that our method outperformed the conventional semi-BSS using ICA under simulated normal and highly reverberative environments.