Several novel double-walled carbon nanotubes (DWCNT) composed of different internal and external nanotubes with different diameters are presented and studied by molecular dynamics simulation (MD). Initial equilibrium configurations and characteristics during free relaxation are examined. Buckling of these DWCNTs under axial compression are simulated to examine the influence of van der Waals force on mechanical properties of DWCNTs. The interaction of atoms in each wall and the van der Waals force between inner and outer walls are described by Tersoff-Brenner potential and Lennard-Jones potential respectively. Results show that new stable DWCNTs exist whose interlayer distances are not necessarily 0.34 nm. And these new DWCNTs show different mechanical behaviors as compared with the normal DWCNT.