In this paper, we present a new parallel accurate algorithm called PAccSumK for computing summation of floating-point numbers. It is based on AccSumK algorithm. In the experiment, for the summation problems with large condition numbers, our algorithm outperforms in term of accuracy and computing time the PSumK algorithm. The reason is that our algorithm is based on a more accurate algorithm called AccSumK algorithm compared to the SumL algorithm used in PSumK. The proposed parallel algorithms in this paper is designed to compute a result as if computed internally in K-fold the working precision. Numerical results are presented showing the performance and the accuracy of our new parallel algorithm for calculating summation.