For two odd integers l, k with 0 < l < k and gcd(l, k) = 1, let m = 2k and d = (2^{lk}+1)/(2^l+1)+2(2^m−1)/3. In this paper, we determine the value distribution of the exponential sum \sum_{x∈F_{2^m }}(−1)^{Tr^m_1 (ax+bx^d)}. As applications, t