In this article, we introduce a variational demosaicking model that restores full-color images from sampled data acquired with a RGBW color filter array (CFA). The proposed model employs the concept of the low-dimensional patch manifold model (LDMM) in Shi et al. (J Sci Comput 75(2):638–656, 2018) and inter-channel correlation terms. The LDMM enables regions without color data to be filled out smoothly from given sparse data, while conserving textures. Moreover, the inter-correlation terms defined in the gradient domain help diminish color artifacts in demosaicked images. We also present an efficient iterative algorithm for solving the proposed model. Numerical experiments validate the effectiveness of our model for demosaicking images acquired with RGBW CFAs as compared to the state-of-the-art models.