The FastSound project is a galaxy redshift survey using Subaru/FMOS to detect Hα emitting galaxies at z ~ 1.3, for the purpose of probing the origin of the accelerated expansion of the universe. The survey has detected ~4,000 galaxy redshifts in a total area of 30 deg2, and detected the redshift space distortion at this redshift range for the first time. The redshift space distortion (RSD) signal will be used to derive a measurement of the growth rate of large scale structure, which will provide a test for modified gravity as a possible origin of accelerated cosmic explansion. Here we present an overview and the current status of the project.