A new sensor made of a vinyl-ester polymer composite filled with multilayer graphene nanoplatelets (MLG) is produced through an innovative capillary rise method for application in strain sensing and structural health monitoring. The new sensor is characterized by high stability of the piezoresistive response under quasi-static consecutive loading/unloading cycles and monotonic tests. This is due to the peculiarity of the fabrication process that ensures a smooth and clean surface of the sensor, without the presence of filler agglomerates acting as micro- or macro-sized defects in the composite.