Today's VidSGG models are all proposal-based methods, i.e., they first generate numerous paired subject-object snippets as proposals, and then conduct predicate classification for each proposal. In this paper, we argue that this prevalent proposal-based framework has three inherent drawbacks: 1) The ground-truth predicate labels for proposals are partially correct. 2) They break the high-order relations among different predicate instances of a same subject-object pair. 3) VidSGG performance is upper-bounded by the quality of the proposals. To this end, we propose a new classification-then-grounding framework for VidSGG, which can avoid all the three overlooked drawbacks. Meanwhile, under this framework, we reformulate the video scene graphs as temporal bipartite graphs, where the entities and predicates are two types of nodes with time slots, and the edges denote different semantic roles between these nodes. This formulation takes full advantage of our new framework. Accordingly, we further propose a novel BIpartite Graph based SGG model: BIG. Specifically, BIG consists of two parts: a classification stage and a grounding stage, where the former aims to classify the categories of all the nodes and the edges, and the latter tries to localize the temporal location of each relation instance. Extensive ablations on two VidSGG datasets have attested to the effectiveness of our framework and BIG.