For any integer k $geq$ 2, let P(c, k + 1;q) be the number of all k+1-tuples with positive integer coordinates ($a_1,a_2,...,a_{k+1}$) such that $1{leq}a_i{leq}q$, ($a_i,q$) = 1, $a_1a_2...a_{k+1}{equiv}$ c (mod q) and 2 $ mid$ ($a_1+a_2+...+a_{k+1}$), and E(c, k+1; q) = P(c, k+1;q) - $frac{{phi}^k(q)}{2}$. The main purpose of this paper is using the properties of Gauss sums, primitive characters and the mean value theorems of Dirichlet L-functions to study the hybrid mean value of the r-th hyper-Kloosterman sums Kl(h,k+1,r;q) and E(c,k+1;q), and give an interesting mean value formula.