Blue phosphorus is a new graphene-like material which has already been proven thermostable in theory, and the synthesis of it on experiment can also be expected. Here, we have investigated the electronic structures and carrier mobilities of armchair and zigzag monolayer blue phosphorus nanoribbons (PNRs) and nanotubes (PNTs) using density functional theory combined with Boltzmann transport method with relaxation time approximation. It is found that both PNRs and PNTs are indirect-gap semiconductors with a considerable energy gap. The numerical calculation results indicate that the armchair PNTs, zigzag PNTs, and armchair PNRs have the characteristics of p-type semiconductors in electrical conduction, because the hole mobility is over 1 order larger than the electron mobility. However, the electron mobility is greater than the hole mobility in zigzag PNRs. Owing to the existing p x orbitals (in-plane and along ribbon direction), which are very sensitive to the atomic structure strain, the band edges will be significantly changed under strain which results in a linear decrease of the gap of PNRs and PNTs with deformation aggravation. The charge mobilities can also be effectively regulated by the strain.