The decomposition of the Nd-Ce-Fe-B phase to form CeFe2 has been usually believed to have an important positive effect on the magnetic properties of Nd-Ce-Fe-B permanent magnetic materials. In this work, a new decomposition process of the Nd-Ce-Fe-B phase on the formation of the CeFe2 phase was observed to play a negative role in its magnetic properties. It is demonstrated that the Nd-Ce-Fe-B phase decomposes into non-magnetic CeFe2, accompanied by the precipitation of Fe soft-phase. The kinks usually occurring in the demagnetization curves of Ce-rich Nd-Ce-Fe-B magnets have been determined to be related to the Fe soft-phase. Instead of using CeFe2 as a grain-boundary phase, another Ce-Cu boundary phase has been explored to efficiently improve the coercivity of Ce-rich Nd-Ce-Fe-B magnets, provided that the Ce-Cu boundary phase has an appropriate Ce to Cu ratio. The present results contribute to the mechanism comprehension and high-performance design of Nd-Ce-Fe-B permanent magnetic materials.