Electromechanical response of materials is a key property for various applications ranging from actuators to sophisticated nanoelectromechanical systems. Here electromechanical properties of the single-layer graphene transferred onto SiO2 calibration grating substrates is studied via piezoresponse force microscopy and confocal Raman spectroscopy. The correlation of mechanical strains in graphene layer with the substrate morphology is established via Raman mapping. Apparent vertical piezoresponse from the single-layer graphene supported by underlying SiO2 structure is observed by piezoresponse force microscopy. The calculated vertical piezocoefficient is about 1.4nmV-1, that is, much higher than that of the conventional piezoelectric materials such as lead zirconate titanate and comparable to that of relaxor single crystals. The observed piezoresponse and achieved strain in graphene are associated with the chemical interaction of graphene's carbon atoms with the oxygen from underlying SiO2. The results provide a basis for future applications of graphene layers for sensing, actuating and energy harvesting.