  In order to constrain $f(R,L_{m})$ gravity from theoretical aspects, its
energy conditions are derived in this paper. These energy conditions given by
us are quite general and can be degenerated to the well-known energy conditions
in General Relativity and $f(R)$ theories of gravity with arbitrary coupling,
non-minimal coupling and non-coupling between matter and geometry,
respectively, as special cases. To exemplify how to use these energy conditions
to restrict $f(R,L_{m})$ gravity, we consider a special model in the FRW
cosmology and give some corresponding results by using astronomical
observations.
