Oscillations that propagate throughout a plant have severe impacts on an industrial process. However, it is still an open problem to design a time-frequency analyzing tool that can characterize the amplitude, frequency, and trend information on the nonstationary plant-wide oscillations. Motivated by this difficulty, a novel algorithm, multivariate intrinsic time-scale decomposition (MITD), is proposed. At first, a sifting process is added into the standard intrinsic time-scale decomposition (ITD), ensuring each of the decomposed product to be a monocomponent. Then, the multivariate ITD is extended from the modified ITD by solving an overdetermined system of linear equations. The advantage of the developed method is that the investigated multidimensional signal can be analyzed under both time and frequency scales. Unlike traditional methods, MITD is able to capture both the regularity of plant-wide oscillations and evolution of local characteristics. It is also capable of automatically clustering the variables having similar oscillations, even when multiple plant-wide oscillations occur. The validity of the raised approach is demonstrated on a series of simulations as well as an industrial case.