For electricity market participants, proper information on the current grid topology is helpful for applications such as locational marginal price (LMP)/congestion forecasting, valuation of electricity derivatives, and operation of generation/distribution assets. However, in many markets, the publication of the grid topology is usually untimely or incomplete due to confidentiality concerns. To solve this problem, this paper proposes an online approach for recovering the latest complete grid topology from timely LMP data and incomplete partial topology information. Under the assumption that the grid topology is sparse, the recovery problem is formulated as a semidefinite programming (SDP) problem. The online alternating direction method (OADM) is applied to obtain a recursive expression for the optimal solution. Case studies on the IEEE 30-bus and 118-bus systems demonstrate the effectiveness and efficiency of the proposed approach.