In order to speed up the wide-spread proliferation of the 3D video technologies (e.g., coding, transmission, display, etc), the effect of these technologies on 3D perception should be efficiently and reliably investigated. Using Full-Reference (FR) objective metrics for this investigation is not practical especially for "on the fly" 3D perception evaluation. Thus, a Reduced Reference (RR) metric is proposed to predict the depth perception of 3D video in this paper. The color-plus-depth 3D video representation is exploited for the proposed metric. Since the significant depth levels of the depth map sequences have great influence on the depth perception of users, they are considered as side information in the proposed RR metric. To determine the significant depth levels, the depth map sequences are abstracted using bilateral filter. Video Quality Metric (VQM) is utilized to predict the depth perception ensured by the significant depth levels due to its well correlation with the Human Visual System (HVS). The performance assessment results present that the proposed RR metric can be utilized in place of a FR metric to reliably measure the depth perception of 3D video with a low overhead.