An increasing demand of magnetic field sensors with high sensitivity at room temperatures and spatial resolution at micro-nanoscales has resulted in numerous investigations of physical phenomena in advanced materials, and fabrication of novel magnetoresistive devices. In this study the novel magnetic field sensor based on combination of a single layer graphene (SLG) and thin nanostructured manganite La0.8Sr0.2MnO3 (LSMO) film-hybrid graphene-manganite (GM) structure, is proposed and fabricated. The hybrid GM structure employs the properties of two materials-SLG and LSMO-on the nanoscale level and results in the enhanced sensitivity to magnetic field of the hybrid sensor on the macroscopic level. Such result is achieved by designing the hybrid GM sensor in a Wheatstone half-bridge which enables to employ in the device operation two effects of nanomaterials-large Lorentz force induced positive magnetoresistance of graphene and colossal negative magnetoresistance of nanostructured manganite film, and significantly increase the sensitivity S of the hybrid GM sensor in comparison with the individual SLG and LSMO sensors: S = 5.5 mV T-1 for SLG, 14.5 mV T-1 for LSMO and 20 mV T-1 for hybrid GM at 0.5 T, when supply voltage was 1.249 V. The hybrid GM sensor operates in the range of (0.1-2.3) T and has lower sensitivity to temperature variations in comparison to the manganite sensor. Moreover, it can be applied for position sensing. The ability to control sensor's characteristics by changing technological conditions of the fabrication of hybrid structure and tuning the nanostructure properties of manganite film is discussed.