  In this paper, we investigate the $L^{p}$-boundedness of the Riesz means and
the $L^{p_{1}}\times L^{p_{2}}\rightarrow L^{p}$ boundedness of the bilinear
Riesz means on M\'{e}tivier groups. M\'{e}tivier groups are generalization of
Heisenberg groups and general H-type groups. Because general M\'{e}tivier
groups only satisfy the non-degeneracy condition and have high-dimensional
centre, we have to use different methods and techniques from those on
Heisenberg groups and H-type groups.
