1. A vehicle side and rear monitoring system with a fail-safe function, comprising: first connection units including imaging device controllers connected to side-view imaging devices of a vehicle, the imaging device controllers configured to display an image captured by the side-view imaging devices on side-view monitors disposed at a side within the vehicle; and a second connection unit including a controller connected to an around view monitoring (AVM) imaging devices, the controller configured to display an image captured by the AVM camera on an AVM monitor located within the vehicle, wherein the controller is configured to determine whether an abnormality occurs in the first connection units, display the image captured through the second connection unit on the side-view monitors when the abnormality occurs in the first connection units, and perform an image rotation transformation after distortion of the image captured by the AVM imaging device is corrected when the image is displayed on the side-view monitors through the second connection unit.