The present invention discloses a method for cryopreservation of human spermatozoa: the method comprises providing spermatozoa free from seminal liquid; mixing the spermatozoa with vitrification medium, wherein the main cryoprotectant agent is 0.1 -0.3 M sucrose; placing the sample inside straws and rapidly freezing them; refrigerating the straws with no need of liquid N2; and devitrifying the sample in a medium of the present invention. The present invention furthermore discloses a portable kit that makes easy to implement the method, said kit comprising vitrification and devitrification solutions in the volumes required to develop the method and the physical support to carry out the same, i.e. the straws. The use of this kit is also disclosed for the treatment of disorders related to reproductive failures.