Traditional rigid endoscopes have challenges in flexibly treating tumors located deep in the brain, and low operability and fixed viewing angles limit its development. This study introduces a novel dual-segment flexible robotic endoscope MicroNeuro, designed to perform biopsies with dexterous surgical manipulation deep in the brain. Taking into account the uncertainty of the control model, an image-based visual servoing with online robot Jacobian estimation has been implemented to enhance motion accuracy. Furthermore, the application of model predictive control with constraints significantly bolsters the flexible robot’s ability to adaptively track mobile objects and resist external interference. Experimental results underscore that the proposed control system enhances motion stability and precision. Phantom testing substantiates its considerable potential for deployment in neurosurgery.