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Let $l⩾2$ be an integer. Recently, Hu and Lü offered the asymptotic formula for the sum of the higher divisor function $$\sum _{1⩽n_1,n_2,...,n_l⩽x^{1/2}}{\tau }_k(n_1^2+n_2^2+\cdots +n_l^2),$$ where ${\tau }_k\left(n\right)$ represents the $k$th divisor function. We give the Goldbach-type analogy of their result. That is to say, we investigate the asymptotic behavior of the sum $$\sum _{1⩽p_1,p_2,...,p_l⩽x}{\tau }_k(p_1+p_2+\cdots +p_l),$$ where $p_1,p_2,\cdots ,p_l$ are prime variables.