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Earth's magnetic field, which is generated in the liquid outer core through the dynamo action, undergoes changes on timescales of a few years to several million years, yet the underlying mechanisms responsible for the field variations remain to be elucidated. In this study, we apply a novel data analysis technique developed in fluid dynamics, namely the dynamic mode decomposition, to analyze the geomagnetic variations over the last two decades when continuous satellite observations are available. The dominant dynamic modes are extracted by solving an eigen-value problem, so one can identify modes with periods longer than the time span of data. Our analysis show that similar dynamic modes are extracted from the geomagnetic secular variation and secular acceleration, justifying the validity of applying the dynamic mode decomposition method to geomagnetic field. We reveal that the geomagnetic field variations are characterized by a global mode with period of 58 years, a localized mode with period of 16 years and an equatorially trapped mode with period of 8.5 years. These modes are possibly related to magnetohydrodynamic waves in the Earth's outer core.