Objective: Using functional magnetic resonance imaging (fMRI) and deep learning to discover the spatial pattern of brain function, or functional brain networks (FBNs) has been attracted many reseachers. Most existing works focus on static FBNs or dynamic functional connectivity among fixed spatial network nodes, but ignore the potential dynamic/time-varying characteristics of the spatial networks themselves. And most of works based on the assumption of linearity and independence, that oversimplify the relationship between blood-oxygen level dependence signal changes and the heterogeneity of neuronal activity within voxels. Approach: To overcome these problems, we proposed a novel spatial-wise attention (SA) based method called Spatial and Channel-wise Attention Autoencoder (SCAAE) to discover the dynamic FBNs without the assumptions of linearity or independence. The core idea of SCAAE is to apply the SA to generate FBNs directly, relying solely on the spatial information present in fMRI volumes. Specifically, we trained the SCAAE in a self-supervised manner, using the autoencoder to guide the SA to focus on the activation regions. Experimental results show that the SA can generate multiple meaningful FBNs at each fMRI time point, which spatial similarity are close to the FBNs derived by known classical methods, such as independent component analysis. Main results: To validate the generalization of the method, we evaluate the approach on HCP-rest, HCP-task and ADHD-200 dataset. The results demonstrate that SA mechanism can be used to discover time-varying FBNs, and the identified dynamic FBNs over time clearly show the process of time-varying spatial patterns fading in and out. Significance: Thus we provide a novel method to understand human brain better. Code is available at https://github.com/WhatAboutMyStar/SCAAE.