In this article a Bayesian methodology (parametric and nonparametric) is proposed in order to estimate, by means of calibration, the population total from a sample with unequal inclusion probabilities. By means of some simulation studies, it was empirically determined that, through an adequate choice of an prior distribution with the proposed methodology, unbiased estimators are obtained. In addition to this, with an appropriate sample size, a smaller variance and confidence intervals with higher levels and minor length were obtained in comparison with the intervals induced by classic estimators (Horvitz-Thompson and calibration estimators). Finally, the implementation of the methodology to estimate the income is exemplified using real data from a labor force survey in Colombia.