  In this article, we prove the Riesz - Fej\'er inequality for complex-valued
harmonic functions in the harmonic Hardy space ${\bf h}^p$ for all $p > 1$. The
result is sharp for $p \in (1,2]$. Moreover, we prove two variant forms of
Riesz-Fej\'er inequality for harmonic functions, for the special case $p=2$.
