  We have successfully implemented the first simultaneous magneto-optical
trapping (MOT) of lithium ($^6$Li) and ytterbium ($^{174}$Yb) atoms, towards
production of ultracold polar molecules of LiYb. For this purpose, we developed
the dual atomic oven which contains both atomic species as an atom source and
successfully observed the spectra of the Li and Yb atoms in the atomic beams
from the dual atomic oven. We constructed the vacuum chamber including the
glass cell with the windows made of zinc selenium (ZnSe) for the CO$_2$ lasers,
which are the useful light sources of optical trapping for evaporative and
sympathetic cooling. Typical atom numbers and temperatures in the compressed
MOT are 7$\times10^3$ atoms, 640 $\mu$K for $^6$Li, 7$\times10^4$ atoms and 60
$\mu$K for $^{174}$Yb, respectively.
