Bioinspired intelligent algorithm (BIA) is a kind of intelligent computing method, which is with a more lifelike biological working mechanism than other types. BIAs have made significant progress in both understanding of the neuroscience and biological systems and applying to various fields. Mobile robot control is one of the main application fields of BIAs which has attracted more and more attention, because mobile robots can be used widely and general artificial intelligent algorithms meet a development bottleneck in this field, such as complex computing and the dependence on high-precision sensors. This paper presents a survey of recent research in BIAs, which focuses on the research in the realization of various BIAs based on different working mechanisms and the applications for mobile robot control, to help in understanding BIAs comprehensively and clearly. The survey has four primary parts: a classification of BIAs from the biomimetic mechanism, a summary of several typical BIAs from different levels, an overview of current applications of BIAs in mobile robot control, and a description of some possible future directions for research.