Metasurfaces represent a new paradigm in artificial subwavelength structures due to their potential to overcome many challenges typically associated with bulk metamaterials. The ability making very thin structures and change their properties dynamically make metasurfaces an exceptional meta-optics platform for engineering advanced electromagnetic and photonic metadevices. Here, we suggest and demonstrate experimentally a novel tunable metasurface capable to enhance significantly the local image quality in magnetic resonance imaging (MRI). We present a design of the hybrid metasurface based on electromagnetically-coupled dielectric and metallic elements. We demonstrate how to tailor the spectral characteristics of the metasurface eigenmodes by changing dynamically the effective permittivity of the structure. By maximizing a coupling between metasurface eigenmodes and transmitted and received fields in the MRI system, we enhance the device sensitivity that results in a substantial improvement of the image quality.