Molecular neuromorphic devices composed of single-walled carbon nanotubes (SWNTs) complexed with polyoxometalate (POM) exhibit various properties very similar to the functions of neurons. A random and extremely dense SWNT/POM network is expected to have the rudimentary ability of reservoir computing, which is a recently introduced framework derived from recurrent neural networks. We performed RC using multiple signals collected from a SWNT/POM random network. The results are expected to contribute to the design and fabrication of SWNT/molecular networks with high reservoir functionalities for future development. A physical reservoir consisting of nanomaterials may become a computing system with low cost, low power consumption, and highly integrated hardware devices for increasingly important edge computing.