Focal adhesions (FAs) are integrin-based transmembrane assemblies that connect a cell to its extracellular matrix (ECM). They are mechanosensors through which cells exert actin cytoskeleton-mediated traction forces to sense the ECM stiffness. Interestingly, FAs themselves are dynamic structures that adapt their growth in response to mechanical force. It is unclear how the cell manages the plasticity of the FA structure and the associated traction force to accurately sense ECM stiffness. Strikingly, FA traction forces oscillate in time and space, and govern the cell mechanosensing of ECM stiffness. However, precisely how and why the FA traction oscillates is unknown. We developed a model of FA growth that integrates the contributions of the branched actin network and stress fibers (SFs). Using the model in combination with experimental tests, we show that the retrograde flux of the branched actin network promotes the proximal growth of the FA and contributes to a traction peak near the FA's distal tip. The resulting traction gradient within the growing FA favors SF formation near the FA's proximal end. The SF-mediated actomyosin contractility further stabilizes the FA and generates a second traction peak near the center of the FA. Formin-mediated SF elongation negatively feeds back with actomyosin contractility, resulting in central traction peak oscillation. This underpins the observed FA traction oscillation and, importantly, broadens the ECM stiffness range over which FAs can accurately adapt to traction force generation. Actin cytoskeleton-mediated FA growth and maturation thus culminate with FA traction oscillation to drive efficient FA mechanosensing.