Recently, most of the existing mobile robot indoor positioning systems (IPSs) use infrared sensors, cameras, and other extra infrastructures. They usually suffer from high cost and special hardware implementation. In order to address the above problems, this article proposes a Wi-Fi-based indoor mobile robot positioning system and designs and develops a robot positioning platform based on the commercial Wi-Fi devices, such as Wi-Fi routers. Furthermore, a robust principal component analysis-based extreme learning machine algorithm is proposed to address the issue of noisy measurements in IPSs. Real-world robot indoor positioning experiments are extensively carried out and the results verify the effectiveness and superiority of the proposed system.