Context. Galaxy imaging surveys observe a vast number of objects, which are ultimately affected by the instrument’s point spread function (PSF). It is weak lensing missions in particular that are aimed at measuring the shape of galaxies and PSF effects represent an significant source of systematic errors that must be handled appropriately. This requires a high level of accuracy at the modelling stage as well as in the estimation of the PSF at galaxy positions.Aims. The goal of this work is to estimate a PSF at galaxy positions, which is also referred to as a non-parametric PSF estimation and which starts from a set of noisy star image observations distributed over the focal plane. To accomplish this, we need our model to precisely capture the PSF field variations over the field of view and then to recover the PSF at the chosen positions.Methods. In this paper, we propose a new method, coined Multi-CCD (MCCD) PSF modelling, which simultaneously creates a PSF field model over the entirety of the instrument’s focal plane. It allows us to capture global as well as local PSF features through the use of two complementary models that enforce different spatial constraints. Most existing non-parametric models build one model per charge-coupled device, which can lead to difficulties in capturing global ellipticity patterns.Results. We first tested our method on a realistic simulated dataset, comparing it with two state-of-the-art PSF modelling methods (PSFEx and RCA) and finding that our method outperforms both of them. Then we contrasted our approach with PSFEx based on real data from the Canada-France Imaging Survey, which uses the Canada-France-Hawaii Telescope. We show that our PSF model is less noisy and achieves a ∼22% gain on the pixel’s root mean square error with respect to PSFEx.Conclusions. We present and share the code for a new PSF modelling algorithm that models the PSF field on all the focal plane that is mature enough to handle real data.