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.
