Blind source separation （BSS） algorithm is utilized in extracting and recovering source signals from mixed signals. Among many different BSS algorithms， the principal skewness analysis （PSA） is a BSS algorithm taking third-order statistics as the objective function. One of its advantages is that its calculation speed is faster than the conventional BSS algorithms. However， because of the serial calculation method， error accumulation exists in the calculation process. In order to solve this problem， this paper proposes an algorithm called parallel PSA. In this algorithm， parallel calculation is used instead of serial calculation， and the corresponding directions of each independent component can be estimated simutaneously， so the problem of error accumulation is avoided. Simulation results prove that， compared with the PSA algorithm， the parallel PSA algorithm not only maintains the fast calculation speed， but also improves the estimation accuracy of each source signal.