Van der Waals heterostructures composed of low-dimensional atomic layers host rich physics for new device applications, such as magic-angle twisted bilayer graphene and coaxial multi-walled hetero-nanotubes. Aside from exploring their abnormal physical behavior, fabrication of such structures also presents a great challenge to this area, owing to the subtle and sensitive interactions among neighboring layers. Here we show by molecular dynamics simulations that narrow blue phosphorene nanoribbons can be encapsulated into carbon nanotubes driven by van der Waals interactions and form one-dimensional heterostructures. It shows that by varying carbon nanotube diameters and nanoribbon width, the nanoribbons can either retain their original straight structures or twist into tubular structures. Wrapping phases are also observed for large-sized blue phosphorus. It is found that the underlying mechanism originates from the competition between van der Waals energy and bending energy induced by tube curvature. A phase diagram of the resultant 1D structure is thus obtained based on a simple analysis of energetics. The results are expected to stimulate further experimental efforts in fabricating one-dimensional van der Waals heterostructues with desired functionality.