  We use both mass and internal energy specified rubidium atoms to jointly test
the weak equivalence principle (WEP). We improve the four-wave
double-diffraction Raman transition method (FWDR) we proposed before to select
atoms with certain mass and angular momentum state, and perform dual-species
atom interferometer. By combining $^{87}$Rb and $^{85}$Rb atoms with different
angular momenta, we compare the differential gravitational acceleration of
them, and determine the value of E\"{o}tv\"{o}s parameter, $\eta$, which
measures the strength of the violation of WEP. For one case
($^{87}$Rb$|\emph{F}=1\rangle$ - $^{85}$Rb$|\emph{F}=2\rangle$),the statistical
uncertainty of $\eta$ is $1.8 \times 10^{-10}$ at integration time of 8960 s.
With various systematic errors correction, the final value is $\eta=(-4.4 \pm
6.7) \times 10^{-10}$. Comparing with the previous WEP test experiments using
atoms, this work gives a new upper limit of WEP violation for $^{87}$Rb and
$^{85}$Rb atom pairs.
