  We present an infinite Grassmann time-evolving matrix product operator method
for quantum impurity problems, which directly works in the steady state. The
method embraces the well-established infinite matrix product state algorithms
with the recently developed GTEMPO method, and benefits from both sides: it
obtains real-time Green's functions without sampling noises and bath
discretization error, it is applicable for any temperature without the sign
problem, its computational cost is independent of the transient dynamics and
does not scale with the number of baths. We benchmark the method on the
finite-temperature equilibrium Green's function in the noninteracting limit
against exact solutions and in the single-orbital Anderson impurity model
against GTEMPO calculations. We also study the zero-temperature non-equilibrium
steady state of an impurity coupled to two baths with a voltage bias, obtaining
consistent particle currents with existing calculations. The method is ideal
for studying steady-state quantum transport, and can be readily used as an
efficient real-time impurity solver in the dynamical mean field theory and its
non-equilibrium extension.
