Vertical transverse oscillations of a coronal magnetic rope, observed simultaneously in the 171 A and 304 A bandpasses of the Atmospheric Imaging Assembly on board the Solar Dynamics Observatory (SDO), are detected. The oscillation period is about 700 s and the displacement amplitude is about 1 Mm. The oscillation amplitude remains constant during the observation. Simultaneous observation of the rope in the bandpasses corresponding to the coronal and chromospheric temperatures suggests that it has a multi-thermal structure. Oscillatory patterns in 171 A and 304 A are coherent, which indicates that the observed kink oscillation is collective, in which the rope moves as a single entity. We interpret the oscillation as a fundamental standing vertically polarized kink mode of the rope, while the interpretation in terms of a perpendicular fast wave could not be entirely ruled out. In addition, the arcade situated above the rope and seen in the 171 A bandpass shows an oscillatory motion with the period of about 1000 s.