Channel knowledge map (CKM) has received widespread attention as an emerging enabling technology for environment-aware wireless communications. It involves the construction of databases containing location-specific channel knowledge, which are then leveraged to facilitate channel state information (CSI) acquisition and transceiver design. In this context, a fundamental challenge lies in efficiently constructing the CKM based on a given wireless propagation environment. Most existing methods are based on stochastic modeling and sequence prediction, which do not fully exploit the inherent physical characteristics of the propagation environment, resulting in low accuracy and high computational complexity. To address these limitations, we propose a Laplacian pyramid (LP)-based CKM construction scheme to predict the channel knowledge at arbitrary locations in a targeted area. Specifically, we first view the channel knowledge as a 2-D image and transform the CKM construction problem into an image-to-image (I2I) inpainting task, which predicts the channel knowledge at a specific location by recovering the corresponding pixel value in the image matrix. Then, inspired by the reversible and closed-form structure of the LP, we show its natural suitability for our task in designing a fast I2I mapping network. For different frequency components of LP decomposition, we design tailored networks accordingly. Besides, to encode the global structural information of the propagation environment, we introduce self-attention and cross-covariance attention mechanisms in different layers, respectively. Finally, experimental results show that the proposed scheme outperforms the benchmark, achieving higher reconstruction accuracy while with lower computational complexity. Moreover, the proposed approach has a strong generalization ability and can be implemented in different wireless communication scenarios.