At the very late design stage, engineering change order (ECO) leakage optimization is often performed to swap some cells for the ones with lower leakage, e.g. the cells with higher threshold voltage (Vth) or with longer gate length. It is very effective but time consuming due to iterative nature of swap and timing check with correction. We introduce a graph convolutional network (GCN) for quick ECO leakage optimization. GCN receives a number of input parameters that model the current timing information of a netlist as well as the connectivity of the cells in a form of a weighted connectivity matrix. Once it is trained, GCN predicts exact Vth (with Vth given by commercial ECO leakage optimization as a reference) of 83% of cells, on average of test circuits. The remaining 17% of cells are responsible for some negative timing slack. To correct such timing as well as to remove any minimum implant width (MIW) violations, we propose a heuristic Vth reassignment. The combined GCN and heuristic achieve 52% reduction of leakage, which can be compared to 61% reduction from commercial ECO, but with less than half of runtime.