Abnormal effects in GPS broadcast ephemerides can have a significant effect on real-time navigation and positioning solutions that use the orbit and clock error data provided by GPS broadcast ephemerides. This paper describes three types of non-integer-hour navigation data in GPS broadcast ephemeris data. Compared with GPST integer hour data, we find that there are two types of data blocks for non-integer-hour navigation containing gross errors with different levels of precision, which is reflected in the user range accuracy (URA) of the broadcast ephemeris. These gross errors can cause large deviations when using the GPS broadcast ephemeris for orbit calculation and lead to a decrease in the kinematic positioning accuracy. An improved weighting method which is based on the consistency relationship between the URA value and the orbital precision is proposed to improve the positioning accuracy by controlling the effect of gross errors in the broadcast ephemerides. The correction algorithm proposed in this paper was applied to real-time kinematic positioning with shipborne GPS data over the South China Sea. The results showed that the proposed positioning algorithm can effectively reduce the effects of gross errors in the broadcast ephemeris, and significantly improve the accuracy of the navigation and positioning.