［Purposes］A nonlinear cone separation theorem in reflexive Banach space is proposed. ［Methods］The separation theorem is proved by using the correlation properties of the elements of a class of generalized positive linear sets defined in literature. ［Findings］Under the assumption of no convexity, it is proved that two closed cones with some special separation property can be approximated by the zeroth level set of a class of monotone sublinear functions with conic level set defined in the existing literature, and that the closed cones with the separation property of its epsilon-conic neighborhood can also be approximated by the zeroth level set of a function of such functions.［Conclusions］In reflexive Banach space, the two closed cones possessing the separation property can be separated by a certain sublinear function,and the question on the existence of a Bishop-Phelps cone which is close to the given cone is positively answered.