In this paper, we present a novel nonparametric motion flow model that effectively describes a motion trajectory of a human and its application to human robot cooperation. To this end, motion flow similarity measure which considers both spatial and temporal properties of a trajectory is proposed by utilizing the mean and variance functions of a Gaussian process. We also present a human robot cooperation method using the proposed motion flow model. Given a set of interacting trajectories of two workers, the underlying reward function of cooperating behaviors is optimized by using the learned motion description as an input to the reward function where a stochastic trajectory optimization method is used to control a robot. The presented human robot cooperation method is compared with the state-of-the-art algorithm, which utilizes a mixture of interaction primitives (MIP), in terms of the RMS error between generated and target trajectories. While the proposed method shows comparable performance with the MIP when the full observation of human demonstrations is given, it shows superior performance when partial trajectory information is given.