Self-supervised learning methods have been proved effective in the task of real-time stereo depth estimation with the requirement of lower memory space and less computational cost. In this paper, a light-weight adaptive network (LWANet) is proposed by combining the self-supervised learning method to perform online adaptive stereo depth estimation for low computation cost and low GPU memory space. Instead of a regular 3D convolution, the pseudo 3D convolution is employed in the proposed light-weight network to aggregate the cost volume for achieving a better balance between the accuracy and the computational cost. Moreover, based on U-Net architecture, the downsample feature extractor is combined with a refined convolutional spatial propagation network (CSPN) to further refine the estimation accuracy with little memory space and computational cost. Extensive experiments demonstrate that the proposed LWANet effectively alleviates the domain shift problem by online updating the neural network, which is suitable for embedded devices such as NVIDIA Jetson TX2. The relevant codes are available at https://github.com/GANWANSHUI/LWANet