Fast radio bursts (FRBs), bright transients with millisecond durations at ∼GHz and typical redshifts probably >0.8, are likely to be gravitationally lensed by intervening galaxies. Since the time delay between images of strongly lensed FRB can be measured to extremely high precision because of the large ratio ∼109 between the typical galaxy-lensing delay time [Formula: see text] (10 days) and the width of bursts [Formula: see text] (ms), we propose strongly lensed FRBs as precision probes of the universe. We show that, within the flat ΛCDM model, the Hubble constant H0 can be constrained with a ~0.91% uncertainty from 10 such systems probably observed with the square kilometer array (SKA) in <30 years. More importantly, the cosmic curvature can be model independently constrained to a precision of ∼0.076. This constraint can directly test the validity of the cosmological principle and break the intractable degeneracy between the cosmic curvature and dark energy.