  In this paper, both the unpolarized and the polarized $\rho$ meson
generalized parton distributions are investigated in the framework of the
Nambu--Jona-Lasinio model using proper time regularization scheme. The symmetry
properties of $\rho$ meson generalized parton distributions are checked. The
three independent distribution functions in deep inelastic scattering,
$F_1(x)$, $b_1(x)$ and $g_1(x)$, and the Sachs-like charge, magnetic, and
quadruple form factors $G_C(t)$, $G_M(t)$ and $G_Q(t)$, which are the first
Mellin moments of unpolarized generalized parton distributions are obtained. In
addition, the $u$ quark axial vector form factors $\tilde{F}_1^u(t)$ and
$\tilde{F}_2^u(t)$ related to the axial currents from the polarized generalized
parton distributions are studied. The impact parameter dependent parton
distribution functions, which are the two-dimensional Fourier transform of
generalized parton distributions are studied, too. The obtained $\rho$ meson
generalized parton distributions satisfy the required properties well.
