The persistent discrepancy between the various measured values of the Hubble constant is one of the most interesting problems in modern cosmology. This problem, in which a discrepancy of approximately 5σ arises between measurements of the early and late universe, is known as the Hubble Tension. On the other hand, Fast Radio Bursts (FRBs) are high-energy, transient extragalactic phenomena that are sensitive to the Hubble constant through their dispersion measure and therefore offer an alternative approach to alleviating this tension. In this work, we compiled a database of 126 FRBs with confirmed host galaxies, classified into three types based on IllustrisTNG simulations. We used a Bayesian approach to estimate H0 across seven host models. Three models treat the host contribution as independent of z; three others treat it as dependent on z, reflecting the repeating nature of FRB, and apply only to the corresponding subpopulation. The seventh is applied to the entire FRB population, and each FRB is assigned the appropriate host model. The most reliable result was obtained for the model that considers the entire population, distinguishing the repeater type of each FRB. For this last case, we obtained H0=71.36−3.94+3.59 km s−1Mpc−1. Two models of the Milky Way were considered, and the YMW16 model consistently yielded higher H0 values than NE2001 model, ranging from +1.12 to +13.24 km s−1Mpc−1 across different host galaxy assumptions. The H0 values obtained for each repeater type are implausible, suggesting that further modeling may be needed for these subpopulations. Finally, we used a catalog of 500 synthetic FRBs that allowed us to generate a deviation of 2.6% from the value obtained with the observed data, but allowed us to decrease the statistical precision from 5.5% to 1.2%, thus demonstrating the great potential that FRBs have as an alternative method to alleviate the Hubble Tension.