Multispectral filter arrays (MSFAs) are widely applied to achieve snapshot multispectral imaging on a single image sensor, which causes incomplete data of each channel in the original captured image, and thus a process of estimating missing data named "demosaicking"is needed for high spatial resolution imaging. In a multispectral imaging system equipped with MSFA, as the number of spectral channels increases, the lack of data in the original captured image becomes severer, which brings great challenges to the demosaicking process, and thus classical demosaicking methods for MSFAs often fail to satisfy both reconstructed image quality and computational efficiency. In this paper, we propose a generic demosaicking method for MSFAs based on adaptive frequency domain filtering (AFDF) which achieves high quality of reconstructed images with little computational cost. Experimental results demonstrate that our proposed demosaicking method outperforms the state-of-the-art methods in terms of both quality of reconstructed images and processing time. © 2021 ACM.