1. A gesture recognition device comprising: a motion information generator that generates body part motion information from a motion of a body part obtained by performing detection and tracking of the body part of a user in each of multiple frames of captured image data acquired by capturing images of the user; a prediction processor that previously stores pre-gesture motion model information indicating a reference motion of the body part of the user regarding a pre-gesture motion performed immediately before a gesture, makes a first comparison of comparing the body part motion information generated by the motion information generator with the pre-gesture motion model information, and generates a prediction result regarding the pre-gesture motion represented by the motion of the body part detected by the motion information generator on a basis of a result of the first comparison; and a recognition processor that previously stores gesture model information indicating a reference motion of the body part of the user in the gesture, makes a second comparison of comparing the body part motion information generated by the motion information generator with the gesture model information, and generates a result of recognition of the gesture represented by the motion of the body part detected by the motion information generator on a basis of the prediction result and a result of the second comparison, wherein: the recognition processor transmits the body part motion information immediately before the recognized gesture to the prediction processor, and the prediction processor stores the body part motion information immediately before the recognized gesture as the pre-gesture motion model information.