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We report an improved test of the weak equivalence principle by using asimultaneous $^{85}$Rb-$^{87}$Rb dual-species atom interferometer. We proposeand implement a four-wave double-diffraction Raman transition scheme for theinterferometer, and demonstrate its ability in suppressing common-mode phasenoise of Raman lasers after their frequencies and intensity ratios areoptimized. The statistical uncertainty of the experimental data forE\"{o}tv\"{o}s parameter $\eta$ is $0.8\times10^{-8}$ at 3200 s. With varioussystematic errors corrected the final value is $\eta=(2.8\pm3.0)\times10^{-8}$.The major uncertainty is attributed to the Coriolis effect.

Test of Equivalence Principle at $10^{-8}$ Level by a Dual-species Double-diffraction Raman Atom Interferometer