A magnetic random access memory using magnetic domain drag and giant magnetoresistance (GMR) or tunnel magnetoresistance (TMR) and a method of operating the same, wherein the magnetic random access memory includes a data storage unit including a fixed layer, a non-magnetic layer, and a free layer having two ends; a data input means electrically connected to both ends of the free layer, for applying current to the free layer to input data into the data storage unit; and a data output means electrically connected to the free layer and the fixed layer to output data stored in the data storage unit. Accordingly, a magnetic random access memory according to the present invention has superior performance than one using a switching field to record data.