Semiconductor devices rely on the charge and spin of electrons, but there is another electronic degree of freedom called pseudospin in a two-level quantum system1 such as a crystal consisting of two sublattices2. A potential way to exploit the pseudospin of electrons in pseudospintronics3-5 is to find quantum matter with tunable and sizeable pseudospin polarization. Here, we propose a bipolar pseudospin semiconductor, where the electron and hole states have opposite net pseudospin polarization. We experimentally identify such states in anisotropic honeycomb crystal-black phosphorus. By sublattice interference of photoelectrons, we find bipolar pseudospin polarization greater than 95% that is stable at room temperature. This pseudospin polarization is identified as a consequence of Dirac cones merged in the highly anisotropic honeycomb system6,7. The bipolar pseudospin semiconductor, which is a pseudospin analogue of magnetic semiconductors, is not only interesting in itself, but also might be useful for pseudospintronics.