In order to obtain the numerical solution of fractional order variable coefficients Volterra‐Fredholm integro‐differential equation with weakly singular kernels , an operational matrix method is presented in this paper .An approximate formula which solves solution of arbitrary order weakly singular integral is given by using the definition of Legendre polynomial and some properties . And an operational matrix of fractional derivatives of Legendre polynomial is also obtained . Then the original problem of the equation is changed into a system of algebraic equation through simplifying and descreting the fractional integro‐differential equation . The convergence analysis proves that the method is convergent . The numerical examples show that the approach is effective .%为了求分数阶变系数且带有弱奇异积分核Volterra‐Fredholm积分微分方程的数值解，本文提出了Legendre多项式算子矩阵法，利用Legendre多项式的定义及其性质给出了分数阶微分算子矩阵，同时也给出了任意阶弱奇异积分的近似求积公式。通过简化所求分数阶积分微分方程，并离散化简后的方程，可将原问题转换为求代数方程组的解。收敛性分析证明了本文方法是收敛的，数值算例验证了该方法的有效性。
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