Molecular dynamics simulations are performed to study the translocation of a DNA oligonucleotide in a carbon nanotube (CNT) channel consisting of CNTs of two different diameters. A strong gravitational acceleration field is applied to the DNA molecule and water solvent as an external driving force for the translocation. It is observed that both the CNT channel size and the strength of gravitational field have significant influence on the DNA translocation process. It is found that the DNA oligonucleotide is unable to pass through the (8,8) CNT even under strong gravitational fields, which extends previous finding that DNA cannot be self-inserted into a (8,8) CNT. It is shown that the DNA can pass through the (10,10)-(12,12) and (12,12)-(14,14) CNTs with stronger gravitational field resulting in faster translocation. The translocation time tau is found to follow the inverse power law relationship with the gravitational acceleration a as tau approximately a(-1.21). The energetic analysis of the translocation process shows that there is an energy barrier for DNA translocation into the (10,10) tube from the (14,14) tube, which is in contrast to previous report that DNA can be self-inserted into a (10,10) tube from outside the CNT. This difference with previous report shows that the dynamic behavior of DNA translocation inside a CNT channel is quite different from that of DNA translocation into a CNT from outside the CNT.