Numerical simulation of an atmospheric DC arc under an axial magnetic field (AMF) is performed with a model of unifying the plasma and electrodes. In the model the configuration of the cathodic arc attachment is free. Results are given for a 200A argon arc under 0-0.02T AMF. The simulation results indicate that, with the AMF, the cathode arc attachment shrinks towards its tip. That induces many changes of arc configuration and arc parameters, different from the calculation assuming a fixed cathodic arc attachment: as the AMF increases, the plasma temperature nearby the cathode tip increases higher; the low temperature hollow of plasma nearby the anode expands more intensively in both axial and radial direction; the profile of current density on the anode exhibits a bigger concave shape; arc voltage drop increases more; and more power is delivered to the anode. The elements that cause the changes are discussed.