This paper address the global optimization problem of polynomial mixed-integer nonlinear programs MINLPs. A improved branch-and-prune algorithm based on the Bernstein form is proposed to solve such MINLPs. The algorithm use a new pruning feature based on the Bernstein form, called the Bernstein box and Bernstein hull consistency. The proposed algorithm is tested on a set of 16 MINLPs chosen from the literature. The efficacy of the proposed algorithm is brought out via numerical studies with the previously reported Bernstein algorithms and several state-of-the-art MINLP solvers.