Chebyshev center computation problem, i.e. finding the point which is at minimum distance to a set of given points, on the probability simplex with alpha-divergence distancemeasure is studied. The proposed solution generalizes the ArimotoBlahut (AB) algorithm utilizing Kullback-Leibler divergence to alpha-divergence, and reduces to the AB method as a. 1. Similar to the AB algorithm, themethod is an ascent method with a guarantee onthe objective value (alpha-mutual information or Chebyshev radius) improvement at every iteration. A practical application area for the method is the fusion of probability mass functions lacking a joint probability description. Another application area is the error exponent calculation.