Accurate and robust cephalometric image analysis plays an essential role in orthodontic diagnosis, treatment assessment and surgical planning. This paper proposes a novel landmark localization method for cephalometric analysis using multiscale image patch-based graph convolutional networks. In detail, image patches with the same size are hierarchically sampled from the Gaussian pyramid to well preserve multiscale context information. We combine local appearance and shape information into spatialized features with an attention module to enrich node representations in graph. The spatial relationships of landmarks are built with the incorporation of three-layer graph convolutional networks, and multiple landmarks are simultaneously updated and moved toward the targets in a cascaded coarse-to-fine process. Quantitative results obtained on publicly available cephalometric X-ray images have exhibited superior performance compared with other state-of-the-art methods in terms of mean radial error and successful detection rate within various precision ranges. Our approach performs significantly better especially in the clinically accepted range of 2 mm and this makes it suitable in cephalometric analysis and orthognathic surgery.