The minimum enclosing ball problem means to construct a ball of the minimum radius enclosing a given set of balls in 〖WTBX〗S〖WTBZ〗.We propose the concept of the diameter of a set of balls and give an approximation algorithm solve the diameter. We developthe 1+ε approximation algorithm using coresets. The time complexity of this algorithm is O(nd/ε+d2/ε〖SX(〗32〖SX)〗(1/ε+d)log(1/ε)). We prove the existence of the coresets of size O(1/ε) are unrelated to n and d.