Since more and more multimedia data associated with spoken documents have been made available to the public, spoken document retrieval (SDR) has become an important research subject in the past two decades. The i-vector based framework has been proposed and introduced to language identification (LID) and speaker recognition (SR) tasks recently. The major contribution of the i-vector framework is to reduce a series of acoustic feature vectors of a speech utterance to a low-dimensional vector representation, and then numbers of well-developed postprocessing techniques (such as probabilistic linear discriminative analysis, PLDA) can be readily and effectively used. However, to our best knowledge, there is no research up to date on applying the i-vector framework for SDR or information retrieval (IR). In this paper, we make a step forward to formulate an i-vector based language modeling (IVLM) framework for SDR. Furthermore, we evaluate the proposed IVLM framework with both inductive and transductive learning strategies. We also exploit multi-levels of index features, including word- and subword-level units, in concert with the proposed framework. The results of SDR experiments conducted on the TDT-2 (Topic Detection and Tracking) collection demonstrate the performance merits of our proposed framework when compared to several existing approaches.