Bundle adjustment (BA) occupies a large portion of SfM and visual SLAM's total execution time. Local BA over the latest several keyframes plays a crucial role in visual SLAM. Its execution time should be sufficiently short for robust tracking; this is especially critical for embedded systems with a limited computational resource. This study proposes a learning-based method using a graph network that can replace conventional optimization-based BA and works faster. The graph network operates on a graph consisting of the nodes of keyframes and landmarks and the edges of the latter's visibility from the former. The graph network receives the parameters' initial values as inputs and predicts the updates to their optimal values. We design an intermediate representation of inputs inspired by the normal equation of the Levenberg-Marquardt method. We use the sum of reprojection errors as a loss function to train the graph network. The experiments show that the proposed method outputs parameter estimates with slightly inferior accuracy in 1/60-1/10 of time compared with the conventional BA.