FastSound is a galaxy redshift survey that uses the near-infrared Fiber Multi-Object Spectrograph (FMOS) mounted on the Subaru Telescope, targeting Hα emitters at z∼1.18-1.54 down to the sensitivity limit of Hα flux ∼ 2 × 10-16 erg cm-2 s-1. The primary goal of the survey is to detect redshift space distortion (RSD), to test the general theory of relativity by measuring the growth rate of large-scale structure and to constrain modified gravity models for the origin of the accelerated expansion of the universe. The target galaxies were selected based on photometric redshifts and Hα flux estimates calculated by fitting spectral energy distribution (SED) models to the five optical magnitudes of the Canada-France-Hawaii Telescope Legacy Survey (CFHTLS) Wide catalog. The survey started in 2012 March, and all the observations were completed in 2014 July. In total, we achieved 121 pointings of FMOS (each pointing has a 30′ diameter circular footprint) covering 20.6 deg2 by tiling the four fields of the CFHTLS Wide in a hexagonal pattern. Emission lines were detected from ∼ 4000 star-forming galaxies by an automatic line detection algorithm applied to 2D spectral images. This is the first in a series of papers based on FastSound data, and we describe the details of the survey design, target selection, observations, data reduction, and emission line detections.