  We investigated the ground state properties of a two dimensional Fermi
superfluid with an anisotropic spin-orbit coupling (SOC) using path-integral
field theoretical method. Within the framework of mean-field theory, we
obtained the condensed fraction including contributions from both singlet and
triple pairing fields. We found that for small interaction parameters and large
anisotropic parameters, the total condensed fraction changes non-monotonically
when increasing the strength of SOC and has a global maximum. But this feature
disappears with decreasing the anisotropic parameter and increasing the
interaction parameter. However, condensed fraction always decrease with
increasing the anisotropic parameters. Because of the anisotropy of the SOC,
the superfluid fraction becomes a tensor. We obtained the superfluid fraction
tensor by deriving the effective action of the phase field of the order
parameter. Our numerical results show that for small interaction parameters and
large anisotropic parameters, superfluid fraction of the $x$ component
$\rho_{x}$ has a minimum as a function of the SOC strength. And this minimum of
$\rho_{x}$ disappears when decreasing the anisotropic parameters. In the strong
interaction regime, $\rho_{x}$ always decreases with increasing the strength of
SOC. While for the $y$ component of the superfluid fraction $\rho_{y}$, no
matter how large the interaction parameters and anisotropic parameters are, it
always has a minimum as a function of the SOC strength. As a function of the
anisotropic parameter, for strong SOC strength, $\rho_{x}<\rho_{y}$ with
$\rho_{x}$ having a minimum. For small SOC parameters $\rho_{x}>\rho_{y}$ with
$\rho_{y}$ developing a minimum only in the weak interaction limit.
