We present extensive molecular dynamics simulations of a cationic nanoparticle and a double-stranded DNA molecule to discuss the effect of DNA flexibility on the complex formation of a cationic nanoparticle with double-stranded DNA. Martini coarse-grained models were employed to describe double-stranded DNA molecules with two different flexibilities and cationic nanoparticles with three different electric charges. As the electric charge of a cationic nanoparticle increases, the degree of DNA bending increases, eventually leading to the wrapping of DNA around the nanoparticle at high electric charges. However, a small increase in the persistence length of DNA by 10 nm requires a cationic nanoparticle with a markedly increased electric charge to bend and wrap DNA around. Thus, a more flexible DNA molecule bends and wraps around a cationic nanoparticle with an intermediate electric charge, whereas a less flexible DNA molecule binds to a nanoparticle with the same electric charge without notable bending. This work provides solid evidence that a small difference in DNA flexibility (as small as 10 nm in persistence length) has a substantial influence on the complex formation of DNA with proteins from a biological perspective and suggests that the variation of sequence-dependent DNA flexibility can be utilized in DNA nanotechnology as a new tool to manipulate the structure of DNA molecules mediated by nanoparticle binding.