When a segment of charge density wave (CDW) conductor is submitted to an external electric field, a voltage arises in the neighboring segment where no external electric field is applied. Despite its long-term correlation, the collective mode of a CDW should not extend beyond current injection electrodes; however, the imposed boundary conditions to the sample at the injection current contacts affect the CDW state's far away the region between these latter. A phase gradient ∇φ is established between the region where the CDW slide and the region where it is still pinned (zero electric field); this can destroy the CDW state, hence a mechanism “phase slip” to remove the phase gradient established in the system.In this letter, we present a numerical study based on the Fukuyama-Lee-Rice (FLR) model of the nonlocal phenomenon in a one-dimensional CDW system in the weak pinning limit case.