The cosmic rays above the second knee energy (~$10^{17}$ eV) are expected to be accelerated by extragalactic sources, such as relativistic jets of gamma-ray bursts (GRBs) and active galactic nucleus. The relativistic jets drive a relativistic Weibel mediated shock if the upstream magnetic field is sufficiently weak. External shocks of GRBs can accelerate CRs to $10^{17}$ eV if the magnetic field generated by the Weibel instability around the shock front do not decay in the far downstream region. However, particle-in-cell (PIC) simulations show that the magnetic fields decay rapidly for the Weibel mediated shocks in a uniform plasma. In reality, there are density fluctuations in interstellar or circumstellar medium. In this study, we preformed two-dimensional PIC simulations of relativistic shocks propagating to inhomogeneous electron-positron plasma. We found that the downstream magnetic field keeps a higher values and larger scales than those for the uniform case. Furthermore, sound and entropy waves are excited by interaction of the upstream density fluctuations with the shock, which would accelerate particles to a higher energy by the second-order acceleration. Therefore, the upstream inhomogeneity plays a crucial role in the CR acceleration and generation of the magnetic field in the far downstream region.