We propose a free-resolution probability distributions map (FRPDM) and an FRPDM-based precise vehicle localization method using 3D light detection and ranging (LIDAR). An FRPDM is generated by Gaussian mixture modeling, based on road markings and vertical structure point cloud. Unlike single resolution or multi-resolution probability distribution maps, in the case of the FRPDM, the resolution is not fixed and the object can be represented by various sizes of probability distributions. Thus, the shape of the object can be represented efficiently. Therefore, the map size is very small (61 KB/km) because the object is effectively represented by a small number of probability distributions. Based on the generated FRPDM, point-to-probability distribution scan matching and feature-point matching were performed to obtain the measurements, and the position and heading of the vehicle were derived using an extended Kalman filter-based navigation filter. The experimental area is the Gangnam area of Seoul, South Korea, which has many buildings around the road. The root mean square (RMS) position errors for the lateral and longitudinal directions were 0.057 m and 0.178 m, respectively, and the RMS heading error was 0.281°.