The impact of false information on numerical judgments was examined on young normal subjects by an event-related potential (ERP) experiment. To imitate the judgments in real world, we ensured the subjects acknowledged of the target task. The behavioral results found that both uncertain information and false information assimilated the final estimates: higher after higher anchors and lower after lower anchors; and false information caused a weaker anchoring bias than uncertain information. ERP results provided further electrophysiological evidence for the mechanism of anchoring. In the early phrase, it was an accessibility-dominated process in which two kinds of anchors elicited an N300 component related to the accessibility of anchors propositions. The knowledge relevant to targets joined the process in the late phrase, which caused a larger amplitude of late positive component (LPC) for implausible lower anchors than that for plausible higher anchors. Source analysis showed that medial frontal gyrus, whose activity was suggested to signal the need of adjustment, was more reliable to explain the LPC elicited by implausible lower anchors. Therefore, we suggest that accessibility is facilitated when the external anchor is consistent with the world knowledge, and adjustment is initiated when the external anchor is inconsistent.