In this paper, we further investigate stochastic comparisons of the lifetime of parallel systems with heterogeneous independent Pareto components in term of the star order and convex order. It will be proved that the lifetime of a parallel system with heterogeneous independent components from Pareto model is always smaller than from the lifetime of another parallel system with homogeneous independent components from Pareto model in the sense of convex order. Also, under a general condition on the scale parameters, it is proved a result involving with star order.