  In this note, we present a new method to investigate the positronium states
in ${\rm{QED_3}}$. According to the $\rm{K\ddot{a}ll\acute{e}n-Lehmann}$
spectral representation, the energy eigenvalues of bound states are poles of
the correlation function. Using the chain approximation, we obtain the energy
eigenvalues of the vector positronium states by taking into account the
single-valued branches of multi-valued function. Using the same method, we also
find the electron physical mass at some single-valued branch of multi-value
function. Our results are agreement with the known ones.
