In this paper,estimate of spectra for a class of higher-order differential system is considered.The inequality of the upper bound of the（n＋1）th spectrum is estimated from the former n spectra by using matrix operation,integration by parts,trial function,Rayleigh theorem and inequality estimate,etc.The estimate coefficients do not depend on the measure of the domain in which the problem is concerned.The results expanded the theorems in the bibliography.%考虑一类高阶微分系统谱的带权估计,利用矩阵运算、分部积分、测试函数、Rayleigh定理和不等式估计等方法,获得了用前n个谱来估计第n＋1个谱的上界的不等式,且其估计系数与区间的度量无关,其结论是文献定理的进一步拓展.
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