Molecular dynamics simulations were performed to study dynamics of carbon nanotube (CNT) interacting with biological molecules (DNA oligonucleotide and protein polypeptide) in an aqueous environment. Our results showed that an oligonucleotide or a polypeptide could be spontaneously inserted into a CNT, provided that the tube size is large enough and the oligonucleotide/polypeptide is appropriately aligned with CNT. The van der Waals and hydrophobic forces were found to be important for the insertion process, with the former playing a more dominant role in the CNT-oligonucleotide and CNT-polypeptide interaction. We discussed temperature effect on the filling process and found that higher temperature can accelerate encapsulation of biological molecules. Our study has general implications on filling nanoporous materials with water solutes of molecular cluster or nanoparticles. The encapsulated CNT-oligonucleotide/polypeptide or other CNT based bio-nano-complex can be further exploited for applications such as molecular electronics, sensors, electronic DNA sequencing, and nanotechnology of gene/drug delivery systems.