  Landauer-B\"uttiker formula describes the electronic quantum transports in
nanostructures and molecules. It will be numerically demanding for simulations
of complex or large size systems due to, for example, matrix inversion
calculations. Recently, Chebyshev polynomial method has attracted intense
interests in numerical simulations of quantum systems due to the high
efficiency in parallelization, because the only matrix operation it involves is
just the product of sparse matrices and vectors. Many progresses have been made
on the Chebyshev polynomial representations of physical quantities for isolated
or bulk quantum structures. Here we present the Chebyshev polynomial method to
the typical electronic scattering problem, the Landauer-B\"uttiker formula for
the conductance of quantum transports in nanostructures. We first describe the
full algorithm based on the standard bath kernel polynomial method (KPM). Then,
we present two simple butefficient improvements. One of them has a time
consumption remarkably less than the direct matrix calculation without KPM.
Some typical examples are also presented to illustrate the numerical
effectiveness.
