IP geolocation can provide geographical locations of network users. It is widely used in location-based services (LBS), such as online advertising, account protection, and localized content delivery. Service providers require a cheap, accurate, and fast IP geolocation method. However, existing IP geolocation algorithms rely on high computation or a large number of distributed vantage points to improve accuracy, which is not cost-effective. Therefore, this paper proposes a lightweight and cost-effective IP geolocation method called LiteGeoPro. LiteGeoPro uses only one vantage point to collect network paths and delay information. Landmark locations then propagate along the shortest path with the smallest delay, and the target location is estimated based on its closest router. City-level geolocation results in China and the U.S. networks demonstrate that LiteGeoPro achieves an average accuracy of over 97% on IPv4 and IPv6 networks. Further experimental results on six datasets in IPv4/6 networks show that the median errors of LiteGeoPro range from 0.01 to 8.94 km. Compared with typical geolocation algorithms SLG and MLP-Geo, LiteGeoPro reduces geolocation errors by up to 99%.