In recent years, open-vocabulary (OV) dense visual prediction (such as OV object detection, semantic, instance and panoptic segmentations) has attracted increasing research attention. However, most of existing approaches are task-specific and individually tackle each task. In this paper, we propose a Unified Open-Vocabulary Network (UOVN) to jointly address four common dense prediction tasks. Compared with separate models, a unified network is more desirable for diverse industrial applications. Moreover, OV dense prediction training data is relatively less. Separate networks can only leverage task-relevant training data, while a unified approach can integrate diverse training data to boost individual tasks. We address two major challenges in unified OV prediction. Firstly, unlike unified methods for fixed-set predictions, OV networks are usually trained with multi-modal data. Therefore, we propose a multi-modal, multi-scale and multi-task (MMM) decoding mechanism to better leverage multi-modal data. Secondly, because UOVN uses data from different tasks for training, there are significant domain and task gaps. We present a UOVN training mechanism to reduce such gaps. Experiments on four datasets demonstrate the effectiveness of our UOVN.