Talbot-Lau X-ray phase contrast imaging is a promising technique in biological imaging since it can provide absorption, differential phase contrast, and dark-field images simultaneously. However, high accuracy motorized translation stages and high stability of the imaging system are needed to avoid moiré artifacts in the reconstructed images. In this work, the effects of the stepping errors and the dose fluctuations on the transmission, differential phase contrast, and dark-field images are theoretically derived and systematically summarized. A novel three-step iterative method is designed for image reconstruction in Talbot-Lau interferometry with phase-stepping errors and dose fluctuations. Phase distributions, phase-stepping errors, and dose fluctuation coefficients are iteratively updated via the least square method until the convergence criteria are met. Moiré artifacts are mostly reduced via the proposed method in both the numerical simulations and experiments. The reconstructed images are highly coincident with the ground truth, which verifies the high accuracy of this method. The proposed algorithm is also compared with other moiré artifacts reduction algorithms, which further demonstrates the high precision of this algorithm. This work is beneficial for reducing the strict requirements for the hardware system in the conventional Talbot-Lau interferometry, such as the high accuracy motorized stages and the X-ray tube with high stability, which is significant for advancing the X-ray phase contrast imaging towards the practical medical applications.