In the standard cosmological model , dark matter drives the structure formation and constructs potential wells within which galaxies may form . The baryon fraction in dark halos can reach the universal value ( 15.7 % ) in massive clusters and decreases rapidly as the mass of the system decreases 1 , 2 . The formation of dwarf galaxies is sensitive both to baryonic processes and the properties of dark matter owing to the shallow potential wells in which they form . In dwarf galaxies in the Local Group , dark matter dominates the mass content even within their optical-light half-radii ( r _ { e } \sim 1 kpc ) 3 , 4 . However , recently it has been argued that not all dwarf galaxies are dominated by dark matter 5 , 6 , 7 . Here we report 19 dwarf galaxies that could consist mainly of baryons up to radii well beyond r _ { e } , at which point they are expected to be dominated by dark matter . Of these , 14 are isolated dwarf galaxies , free from the influence of nearby bright galaxies and high dense environments . This result provides observational evidence that could challenge the formation theory of low-mass galaxies within the framework of standard cosmology . Further observations , in particular deep imaging and spatially-resolved kinematics , are needed to constrain the baryon fraction better in such galaxies .