Shape morphing is an attractive functionality for fibre reinforced composites. Shape morphing composites can adopt various shapes and undergo different shape morphologies in response to a set of external stimuli. One of the approaches to attain shape morphing materials is through fabrication of multi-layered and asymmetric composites where morphing stems from structural anisotropy. In this work, asymmetric hybrid carbon fibre/glass fibre/epoxy composites are manufactured in which a mismatch in the coefficient of thermal expansion between carbon and glass fibre layers and different fibre directions at each layer resulted in a thermo-responsive morphing behaviour. The full-field displacement of laminate surfaces at the temperature range of −30 °C to 60 °C are monitored using digital image correlation technique. Classical laminate theory and Timoshenko bimetallic strip formula are coupled with experimental observations to predict the radius of curvature for laminates at different temperatures. Furthermore, finite element analyses are performed to uncover the stress state in the laminates and identify the contributing mechanisms. This study contributes to the state of the art by elaborating on the relations between morphing performance with stiffness and thermal expansion of anisotropic fibre reinforced laminates and their connections to the microstructure.