This paper develops a framework for the safety assessment of bridges based on the nondestructive test (NDT) results of concrete. The transient elastic wave test is performed to measure the P wave velocity of concrete. The Bayesian approach is adopted to construct the posterior distribution of concrete strength. Then, reliability analysis is carried out to evaluate the safety of the bridge using the modified distribution. The limit-state function is formulated according to the AASHTO specifications. Finally, the reliability index is compared to the target reliability to see if repair or reconstruction is required. A numerical example is presented to illustrate the safety assessment of a solid-slab bridge using the proposed method.