Cu is commonly used in the field of electricity and electronics because of its high ductility, and electrical and thermal conductivity. The thermophysical properties and the atomic structure of liquid Cu, especially for undercooled state, are of practical significance in both application and fundamental researches. The major approaches to obtain thermophysical properties of undercooled metals are containerless techniques based on electrostatic levitation, electromagnetic levitation and ultrasonic levitation et al. However, the strong volatility of liquid Cu results in great difficulties to measure the thermophysical properties. Accordingly, computational prediction is becoming an expected method to obtain the thermophysical data of liquid Cu. The molecular dynamics (MD) simulation, in combination with a resonable potential model, has been extensively employed in studying the physical properties of several metals as a powerful approach. In this work, the atomic distribution and thermophysical properties including melting temperature, density, specific heat and self-diffusion coefficient of liquid Cu were studied by molecular dynamics simulation. Mishin's and Zhou's embedded-atom method potentials, and the modified embedded-atom method potential proposed by Baskes were used over the temperature range of 800~2400 K, reaching the maximum undercooling of 556 K. The simulated results are in good agreement with the reported experimental results. The crystal-liquid-crystal sandwich structure has been used to calculate the melting point. The melting point calculated by Baskes' potential model is 1341 K, just a difference of 1.11% from the experimental value. The density at the melting point calculated by Mishin's potential is 7.86 g/cm³, with a difference less than 2% compared with the reported data. It is found that the enthalpy of liquid Cu increases linearly with the increase of temperature. The specific heat is obtained to be 31.89 J/(molK) by Mishin's potential, which is constant in the corresponding temperature range. The self-diffusion coefficient is exponentially dependent on the temperature. The maximum error between the reported value and the present value of the self-diffusion coefficient calculated by Mishin's potential is only 4.93%. The pair distribution function was applied to investigate the atomic structure of liquid Cu, which suggests that the simulated system is still ordered in short range and disordered in long range for both normal liquid and undercooled state. It is found that the atomic ordered degree is weakened with the increase of temperature, and it is kept within 3~4 atom neighbor distance.