Basalt Fiber Reinforced Polymer (BFRP) bar has recently regarded as a promising material alternative to conventional steel bar in marine concrete structure due to its advantageous mechanical and physical properties. In this paper, the failure mechanisms of concrete reinforced with BFRP bars are analyzed and then the bond strength of BFRP bars in concrete based on different failure modes is proposed. Bond strengths corresponding respectively to partial cracking elasticity theory, partial cracking plasticity theory and plasticity theory distinguished well by Logistic method are obtained, in which the influences of concrete strength, bar-diameter, thickness of concrete cover and loading rate are taken into account comprehensively. The prediction accuracies of presented model are finally validated by a series of pull-out tests performed in this work. It is indicated that the bond strengths are sensitive to the failure modes of reinforced block. The failure modes can be predicted theoretically using Logistic method and hence the expressions of bond strength for pull-out failure, splitting failure and rupture failure were further derived. The bar-diameter, cover thickness and loading rate have considerable impacts on the cracking state of enclosing concrete and thus they have significant effects on the bond strength of BFRP bars in concrete. The theoretical values of bond strength are in good agreement with the measured results, a prediction error varying between 0.9% and 23.7%. The relative error was mostly depended on the bar-diameter and loading rate according to range analysis and variance analysis, demonstrating that the bar-diameter and the loading rate were both have remarkable influences on the pull-out behavior of BFRP bar. This work is helpful for understanding the failure mechanisms of BFRP-reinforced concrete and provides a reasonable tool for estimating the bond strengths.