Zhu Yanshou (朱延壽) (870 - 903) was an officer under, and the brother-in-law of, the major warlord Yang Xingmi the military governor (Jiedushi) of Huainan Circuit (淮南, headquartered in modern Yangzhou, Jiangsu) late in the Chinese dynasty Tang Dynasty. He contributed to many of Yang's campaigns and eventually rose to the rank of military governor of Fengguo Circuit (奉國, headquartered in modern Zhumadian, Henan, although Zhu did not actually control it). In 903, angry that Yang had previously insulted him, he plotted to rebel against Yang, along with other vassals of Yang's, Tian Jun the military governor of Ningguo Circuit (寧國, headquartered in modern Xuancheng, Anhui) and An Renyi (安仁義) the military prefect of Run Prefecture (潤州, in modern Zhenjiang, Jiangsu). Their plot was discovered by Yang, who then tricked his wife (Zhu's sister) Lady Zhu into reporting to Zhu Yanshou that Yang was about to entrust Huainan Circuit to him. When Zhu reported to Huainan's capital Yang Prefecture (揚州) in response, Yang Xingmi executed him.
Zhu Yanshou was born in 870 and from Shucheng (舒城, in modern Lu'an, Anhui). He appeared to be the third son among his siblings — with descriptions suggesting that he had younger brothers as well — and he had at least one older sister, who married the Huainan Circuit army officer Yang Xingmi at some point.
It was said that Zhu Yanshou had much contributions serving under Yang Xingmi in Yang's campaigns to eventually rule Huainan, against other contenders Qin Yan, Bi Shiduo, Zhao Huang, and Sun Ru, although the first concrete reference to Zhu's acts was in 891 when Sun, then in control of Huainan's capital Yang Prefecture (揚州), was set to attack Yang Xingmi, who was then at Xuan Prefecture (宣州, in modern Xuancheng, Anhui). Yang Xingmi sent Zhu and Liu Wei (劉威) to engage Sun at Huangchi (黃池, in modern Wuhu, Anhui), but Zhu and Liu were defeated by Sun. (Sun's advances were subsequently hampered by severe flooding, however, and he withdrew.)