Daily life assistance for elderly individuals in hospitals and care facilities is one of the most urgent and promising applications for service robots. Especially, a fetch-and-give task is a frequent and fundamental task for service robots to assist elderlys daily life. In hospitals and care facilities, this task is often performed with a movable platform such as a wagon or a cart to carry and deliver a large amount of objects at once. Thus the navigation and control of not only a service robot but also a movable platform must be planned safely. In addition, a robot motion planning to hand over an object to a person safely and comfortably according to his/her posture is also an important problem in this task, however this has not been discussed so much. In this work, we present a coordinate motion planning technique for a fetch-and-give task using a wagon and a service robot. Handover motion is also planned by considering the manipulability of both a robot and a person. Experiments of a fetch-and-give task using a service robot are successfully carried out.