Let V be an n-dimensional vector space over the finite field F q . Suppose that F is an intersecting family of m-dimensional subspaces of V . The covering number of F is the minimum dimension of a subspace of V which intersects all elements of F. In this paper, we give the tight upper bound for the size of F whose covering number is m, and describe the structure of F which reaches the upper bound. Moreover, we determine the structure of an maximum intersecting family of singular linear space with the maximum covering number.