Omni-directional images have been used in wide range of applications including virtual/augmented realities, self-driving cars, robotics simulators, and surveillance systems. For these applications, it would be useful to estimate saliency maps representing probability distributions of gazing points with a head-mounted display, to detect important regions in the omni-directional images. This paper proposes a novel saliency-map estimation model for the omni-directional images by extracting overlapping 2-dimensional (2D) plane images from omni-directional images at various directions and angles of view. While 2D saliency maps tend to have high probability at the center of images (center bias), the high-probability region appears at horizontal directions in omni-directional saliency maps when a head-mounted display is used (equator bias). Therefore, the 2D saliency model with a center-bias layer was fine-tuned with an omni-directional dataset by replacing the center-bias layer to an equator-bias layer conditioned on the elevation angle for the extraction of the 2D plane image. The limited availability of omni-directional images in saliency datasets can be compensated by using the well-established 2D saliency model pretrained by a large number of training images with the ground truth of 2D saliency maps. In addition, this paper proposes a multi-scale estimation method by extracting 2D images in multiple angles of view to detect objects of various sizes with variable receptive fields. The saliency maps estimated from the multiple angles of view were integrated by using pixel-wise attention weights calculated in an integration layer for weighting the optimal scale to each object. The proposed method was evaluated using a publicly available dataset with evaluation metrics for omni-directional saliency maps. It was confirmed that the accuracy of the saliency maps was improved by the proposed method.