This work focuses on the task of elderly activity recognition, which is a challenging task due to the existence of individual actions and human-object interactions in elderly activities. Thus, we attempt to effectively aggregate the discriminative information of actions and interactions from both RGB videos and skeleton sequences by attentively fusing multimodal features. Recently, some nonlinear multi-modal fusion approaches are proposed by utilizing nonlinear attention mechanism that is extended from Squeeze-and-Excitation Networks (SENet). Inspired by this, we propose a novel Expansion-Squeeze-Excitation Fusion Network (ESE-FN) to effectively address the problem of elderly activity recognition, which learns modal and channel-wise Expansion-Squeeze-Excitation (ESE) attentions for attentively fusing the multi-modal features in the modal and channel-wise ways. Specifically, ESE-FN firstly implements the modal-wise fusion with the Modal-wise ESE Attention (M-ESEA) to aggregate discriminative information in modal-wise way, and then implements the channel-wise fusion with the Channelwise ESE Attention (C-ESEA) to aggregate the multi-channel discriminative information in channel-wise way (referring to Figure 1). Furthermore, we design a new Multi-modal Loss (ML) to keep the consistency between the single-modal features and the fused multi-modal features by adding the penalty of difference between the minimum prediction losses on single modalities and the prediction loss on the fused modality. Finally, we conduct experiments on a largest-scale elderly activity dataset, i.e., ETRI-Activity3D (including 110,000+ videos, and 50+ categories), to demonstrate that the proposed ESE-FN achieves the best accuracy compared with the state-of-the-art methods. In addition, more extensive experimental results show that the proposed ESE-FN is also comparable to the other methods in terms of normal action recognition task.