Centimetres-long carbon nanotube (CNT) bundles with tensile strength over 80 GPa have been fabricated and tested recently [Nat. Nanotechnol. 13, 589–595 (2018)], but it is still a tremendous challenge to predict their nonlinear mechanical behaviors by full-atom molecular dynamics (MD) due to the huge computational cost, particularly for carbon nanotube networks. We completely established here the explicit expressions of the chirality-dependent higher-order nonlinear coarse-grained stretching and bending potentials based on the full-atom Reactive Empirical Bond-Order interatomic potential of second generation (REBO potential). In particular, the coarse-grained non-bonded potentials are improved by using the 18–24 Lennard-Jones potential. By comparison with available experimental results and full-atom MD simulations as well as our analytical results, the present nonlinear coarse-grained potentials have high accuracy. The obtained nonlinear coarse-grained potentials can be used to efficiently characterize the nonlinear mechanical behaviors and understand the failure mechanism of the CNT bundles and networks with 2∼5 orders of magnitude reduction in computing time, which should be of great help for designing and assembling CNT-based flexible microdevices.