Directing the motion of molecules/colloids in any specific direction is of great interest in many applications of chemistry, physics, and biological sciences, where regulated positioning or transportation of materials is highly desired. Using Brownian dynamics simulations of coarse-grained models of a long, double-stranded DNA molecule and positively charged nanoparticles, we observed that the motion of a single nanoparticle bound to and wrapped by the DNA molecule can be directed along a gradient of DNA local flexibility. The flexibility gradient is constructed along a 0.8 kilobase-pair DNA molecule such that local persistence length decreases gradually from 50 nm to 40 nm, mimicking a gradual change in sequence-dependent flexibility. Nanoparticles roll over a long DNA molecule from less flexible regions towards more flexible ones as a result of the decreasing energetic cost of DNA bending and wrapping. In addition, the rolling becomes slightly accelerated as the positive charge of nanoparticles decreases due to a lower free energy barrier of DNA detachment from charged nanoparticle for processive rolling. This study suggests that the variation in DNA local flexibility can be utilized in constructing and manipulating supramolecular assemblies of DNA molecules and nanoparticles in structural DNA nanotechnology.