Two-photon imaging in behaving animals has revealed neuronal activities related to behavioral and cognitive function at single-cell resolution. However, marmosets have posed a challenge due to limited success in training on motor tasks. Here we report the development of protocols to train head-fixed common marmosets to perform upper-limb movement tasks and simultaneously perform two-photon imaging. After 2-5 months of training sessions, head-fixed marmosets can control a manipulandum to move a cursor to a target on a screen. We conduct two-photon calcium imaging of layer 2/3 neurons in the motor cortex during this motor task performance, and detect task-relevant activity from multiple neurons at cellular and subcellular resolutions. In a two-target reaching task, some neurons show direction-selective activity over the training days. In a short-term force-field adaptation task, some neurons change their activity when the force field is on. Two-photon calcium imaging in behaving marmosets may become a fundamental technique for determining the spatial organization of the cortical dynamics underlying action and cognition.