Visual information extraction (VIE) plays an important role in Document Intelligence. Generally, it is divided into two tasks: semantic entity recognition (SER) and relation extraction (RE). Recently, pre-trained models for documents have achieved substantial progress in VIE, particularly in SER. However, most of the existing models learn the geometric representation in an implicit way, which has been found insufficient for the RE task since geometric information is especially crucial for RE. Moreover, we reveal another factor that limits the performance of RE lies in the objective gap between the pre-training phase and the fine-tuning phase for RE. To tackle these issues, we propose in this paper a multi-modal framework, named GeoLayoutLM, for VIE. GeoLayoutLM explicitly models the geometric relations in pre-training, which we call geometric pre-training. Geometric pre-training is achieved by three specially designed geometry-related pre-training tasks. Additionally, novel relation heads, which are pre-trained by the geometric pre-training tasks and fine-tuned for RE, are elaborately designed to enrich and enhance the feature representation. According to extensive experiments on standard VIE benchmarks, GeoLayoutLM achieves highly competitive scores in the SER task and significantly outperforms the previous state-of-the-arts for RE (e.g.,the F1 score of RE on FUNSD is boosted from 80.35% to 89.45%).