Carbon nanotube foams (CNFs) have been successfully used as near-critical-density targets in the laser-driven acceleration of high-energy ions and electrons. Here we report the recent advances in the fabrication technique of such targets. With the further developed floating catalyst chemical vapor deposition (FCCVD) method, large-area ($>25\kern0.5em {\mathrm{cm}}^2$) and highly uniform CNFs are successfully deposited on nanometer-thin metal or plastic foils as double-layer targets. The density and thickness of the CNF can be controlled in the range of $1{-}13\kern0.5em \mathrm{mg}/{\mathrm{cm}}^3$ and $10{-}200\kern0.5em \mu \mathrm{m}$, respectively, by varying the synthesis parameters. The dependence of the target properties on the synthesis parameters and the details of the target characterization methods are presented for the first time.