Anomalous superlattice dark-field images of composite precipitates consisting of a dark core surrounded by a bright shell in Al-2.52Li-0.15Zr alloys, has been investigated by many beam dynamical image simulations employing a scattering matrix approach. The coherency strain field in the shell of the precipitate, as well as in the matrix, has been calculated by use of relations derived, and these are incorporated into the image calculations to determine whether the unexpected images can be elucidated by the coherency strain field of the precipitates. It has been found that the coherency strain field may modify the observed composite precipitate images, but it definitely cannot be the origin of the observed anomaly in these images. It has been also shown by the image matching technique, that the mismatch between the beta’ (Al3Zr) precipitates and aluminium matrix in Al-Li-Zr alloys should have a value of about 0.3%.