The invention discloses a polymer/recombinant human erythropoietin conjugate, wherein the polymer is a derivative of a hydrophilic polymer selected from polyethylene glycol, polypropylene glycol, polyvinyl alcohol, polypropylene morpholine and copolymers of the polyethylene glycol, the polypropylene glycol, the polyvinyl alcohol and the polypropylene morpholine, and the molecular weight of P is between 18,000 and 50, 000 daltons. The invention also discloses a medicine compound containing the conjugate, an application of the conjugate and a preparation method.