The phase transformation behaviors of ultrathin Cu film under uniaxial tensile stress are investigated using molecular dynamic simulation. With the stress increasing, Cu film undergoes a successive phase transformation, i.e. firstly fcc -> bcc, then bcc -> hcp. The phase transformation process is very fast and thorough, i.e., all parents phase can transit into the new phase almost instantaneously. The crystallography mechanisms of two martensitic transformations are exactly corresponding to Bain and Burgers mechanism, respectively. By examining the formation conditions of such phase transformation in Cu film, we reveal that this fcc -> bcc -> hcp successive phase transformation will be subject to the very strict simulation conditions, namely stretching along [100] ( or [010], [001] ) direction, definitive tensile speed (1 x 10(10)/s), appropriate film thickness (0.7230-18.08 nm), low temperature (T <= 10 K), and continuous stretching process without any relaxation procedure.