J1846-0513 is a millisecond pulsar discovered by the Five-hundred-meter Aperture Spherical radio Telescope (FAST) which is stablished by China. Data analysis of observation reveals that the pulsar is harbored in a binary with orbital period of P_orb = 0.613 d and ccentricity of e = 0.208. According to the theory of binary evolution, its eccentricity originates from an asymmetric supernova explosion during which the second neutron star burn. Together with the observed parameters of component mass, the binary is assumed to be a double neutron star system candidate. Considering its importance to understand the evolution of stars and binaries, in current work, we simulated the evolution of neutron star - helium (He) star system with initial mass of 1.345 M⊙ and 2.8 M⊙, respectively, and initial orbital period of 0.5 day.At the end of simulation, the total mass of the He star is reduced to 1.556M⊙ with a carbon-oxygen core with mass of 1.431 M⊙. A silicon core of mass 0.846 M⊙ and an iron/neutron-rich core of mass 0.086M⊙ formed in the He star which illustrate it will end with core collapse supernova and born a neutron star with mass of its lower limit. Subsequent simulation of dynamical effects of the supernova explosion indicates that current model may evolve to the observed eccentric double neutron star candidate.