2D nanomaterials have been attracting extensive research interests due to their superior properties and the accurate thermophysical characterization of 2D materials is very important for nanoscience and nanotechnology. This paper presents a transient "laser flash Raman spectroscopy" method for measuring the thermal diffusivity of 2D nanomaterials in the supported form without knowing the laser absorption coefficient. Square pulsed laser rather than continuous laser is used to heat the sample and the accumulated Raman signals are used to determine the time-averaged temperature rise of both the supported 2D material and the substrate. The laser absorption coefficient can be eliminated by comparing the temperature rises measured with different laser spot sizes and laser pulse durations. The method sensitivity is also analyzed by case studies for typical 2D nanomaterials. This method is useful for measuring the thermophysical properties of 2D materials in the most applicable forms and figuring out the difference between the supported and free-standing 2D material. (C) 2016 Elsevier Ltd. All rights reserved.