In this paper, we propose an improved model of Shallow-UWnet for underwater image enhancement. In the proposed method, we enhance the learning process and solve the vanishing gradient problem by a skip connection, which concatenates the raw underwater image and the low-pass filter (LPF) impulse response into Shallow-UWnet. Additionally, we integrate the simple, parameter-free attention module (SimAM) into each Convolution Block to enhance the visual quality of images. Performance evaluations with state-of-the-art methods show that the proposed method has comparable results on EUVP-Dark, UFO-120, and UIEB datasets. Moreover, the proposed model has fewer trainable parameters and the resulting faster testing time is suitable for real-time processing in underwater image enhancement, particularly for resource-constrained underwater robots.