Abstract Previous studies have shown that iterative in-line X-ray phase retrieval algorithms may have higher precision than direct retrieval algorithms. This communication compares three iterative phase retrieval algorithms in terms of accuracy and efficiency using computer simulations. We found the Fourier transformation based algorithm (FT) is of the fastest convergence, while the Poisson-solver based algorithm (PS) has higher precision. The traditional Gerchberg–Saxton algorithm (GS) is very slow and sometimes does not converge in our tests. Then a mixed FT–PS algorithm is presented to achieve both high efficiency and high accuracy. The mixed algorithm is tested using simulated images with different noise level and experimentally obtained images of a piece of chicken breast muscle.