The noise characteristics of randomly networked single-walled carbon nanotubes grown directly by plasma enhanced chemical vapor deposition (PECVD) are studied with field effect transistors (FETs). Due to the geometrical complexity of nanotube networks in the channel area and the large number of tube-tube/tube-metal junctions, the inverse frequency, 1/f, dependence of the noise shows a similar level to that of a single single-walled carbon nanotube transistor. Detailed analysis is performed with the parameters of number of mobile carriers and mobility in the different environment. This shows that the change in the number of mobile carriers resulting in the mobility change due to adsorption and desorption of gas molecules (mostly oxygen molecules) to the tube surface is a key factor in the 1/f noise level for carbon nanotube network transistors.