Abstract: One of the most important topics in number theory is the study of zeros of L-functions. Near the edge of the critical strip, one may show that the number of zeros for certain L-functions is small; such a result is called a zero density estimate. For Dirichlet L-functions, this topic is well understood by the work of Gallagher, Selberg, Jutila, etc. For families of automorphic L-functions, Kowalski and Michel show that the number of zeros near the edge of the critical strip is small on average. The proof uses a large sieve inequality with key objects called pseudo-characters. I will present my recent progress on the refinement of Kowalski-Michel's large sieve inequality, which gives rise to a better zero density estimate for automorphic L-functions.