The self-assembled two-dimensional random networks composed of isolated SWNTs are obtained by a simple floating catalyst CVD method. A remarkable advantage of this technique is that the random networks can be formed at relatively low temperature with a wide density range, which is distinct from the previous reports. We also find that the deposited SWNTs constituting the networks are isolated rather than in bundles, and this result should be help for improving the preparation technique and exploring the formation mechanism of SWNTs.