An universal scaling between exciton binding energy and band gap was first discovered in two-dimensional semiconductors such as graphene derivatives, various TMDs, and black phosphorus [ PRL 115, 066403 (2015); 118, 266401 (2017) ], and later extended to quasi one-dimensional systems such as carbon nanotubes and graphene nanoribbons. In this work we study the excitonic states in phosphorene atomic chains by using the exact diagonalization method and show that the linear scaling between the exciton binding energy (Ex) and quasiparticle shift (∆qs) can be easily tuned by the dielectric environment. In the presence of weak screening, Ex is seen to increase with ∆qs and exhibits a similar scaling as those 2D materials. As the screening becomes stronger, however, the dependence is found to be reversed, i.e., Ex now decreases when ∆qs increases. More interestingly, we also reveal that Ex may even become nearly constant, independent on the system dimension and ∆qs when the screening reaches a certain strength. These abnormal scaling relations are attributed to the complex nature of excitons in the strongly correlated one-dimensional system.