With recent advancements in cancer research and other branches of medicine, many cancer patients can be clinically cured who will never experience disease recurrence or progression, or disease-specific death. In the presence of a high cure fraction, conventional survival models are not appropriate because they do not account for the possibility of cure. The mixture cure models (MCMs) have been developed with the EM based implementation to simultaneously estimate the cure fraction and the survival function of uncured patients. However, the available R packages for the EM-based implementation of the MCMs are lack of robustness, especially when the sample size is small. This paper investigates the stability of the estimates of the MCMs, and proposes a shrinkage EM algorithm for robust inference of mixture cure models by incorporating existing common knowledge on predictors as weakly informative priors. Numerical studies are conducted to show the instability of the ordinary EM-based estimates of MCMs and the advantages of shrinkage EM algorithm for robust inference of mixture cure models.