Large Vision-Language Models (LVLMs) can accurately locate key objects in images, yet their attention to these objects tends to be very brief. Motivated by the hypothesis that sustained focus on key objects can improve LVLMs' visual capabilities, we propose Cross-Layer Vision Smoothing (CLVS). The core idea of CLVS is to incorporate a vision memory that smooths the attention distribution across layers. Specifically, we initialize this vision memory with position-unbiased visual attention in the first layer. In subsequent layers, the model's visual attention jointly considers the vision memory from previous layers, while the memory is updated iteratively, thereby maintaining smooth attention on key objects. Given that visual understanding primarily occurs in the early and middle layers of the model, we use uncertainty as an indicator of completed visual understanding and terminate the smoothing process accordingly. Experiments on four benchmarks across three LVLMs confirm the effectiveness and generalizability of our method. CLVS achieves state-of-the-art overall performance across a variety of visual understanding tasks and attains comparable results to the leading approaches on image captioning benchmarks.