The cerebellum plays a distinctive role within our motor control system to achieve fine and coordinated motions. While cerebellar lesions do not lead to a complete loss of motor functions, both action and perception are severally impacted. Hence, it is assumed that the cerebellum uses an internal forward model to provide anticipatory signals by learning from the error in sensory states. In some studies, it was demonstrated that the learning process relies on the joint-space error. However, this may not exist. This work proposes a novel fully spiking neural system that relies on a forward predictive learning by means of a cellular cerebellar model. The forward model is learnt thanks to the sensory feedback in task-space and it acts as a Smith predictor. The latter predicts sensory corrections in input to a differential mapping spiking neural network during a visual servoing task of a robot arm manipulator. In this paper, we promote the developed control system to achieve more accurate target reaching actions and reduce the motion execution time for the robotic reaching tasks thanks to the cerebellar predictive capabilities.