Molecular mechanics results show that a hexagonal boron nitride (h-BN) membrane can spontaneously assemble on the single-walled boron nitride nanotube (BNNT) in a scroll or helical manner, showing an interesting dependence on h-BN width. The size of BNNTs should meet the required conditions to guarantee self-assembly. Further analyses of energy components and structural geometry show that this unique phenomenon is because of the combined action of van der Waals interactions and the π-π stacking effect. The h-BNs with arbitrary sizes and shapes can wrap onto BNNTs to form various configurations. The self-assembly conditions and the stability of the formed nanoconfigurations are investigated for numerous potential applications.