  Resistivity and magnetization have been measured at different temperatures
and magnetic fields in organic superconductors
$\kappa$-(BEDT-TTF)$_{2}$Cu[N(CN)$_{2}$]Br. The lower critical field and upper
critical field are determined, which allow to depict a complete phase diagram.
Through the comparison between the upper critical fields with magnetic field
perpendicular and parallel to the conducting ac-planes, and the scaling of the
in-plane resistivity with field along different directions, we found that the
anisotropy $\Gamma$ is strongly temperature dependent. It is found that
$\Gamma$ is quite large (above 20) near $T_{c}$, which satisfies the 2D model,
but approaches a small value in the low-temperature region. The 2D-Tinkham
model can also be used to fit the data at high temperatures. This is explained
as a crossover from the orbital depairing mechanism in high-temperature and
low-field region to the paramagnetic depairing mechanism in the high-field and
low-temperature region. The temperature dependence of lower critical field
$H_{c1} (T)$ shows a concave shape in wide temperature region. It is found that
neither a single $d$-wave nor a single $s$-wave gap can fit the $H_{c1} (T)$,
however a two-gap model containing an $s$-wave and a $d$-wave can fit the data
rather well, suggesting two-band superconductivity and an unconventional
pairing mechanism in this organic superconductor.
